Ze, Li; Qu, Changzheng Global dynamics to the periodic ferromagnetic spin chain system. (English) Zbl 07817074 SIAM J. Math. Anal. 56, No. 2, 1672-1726 (2024). MSC: 35Q60 35Q55 35Q82 35K59 82D40 78A30 35R09 PDFBibTeX XMLCite \textit{L. Ze} and \textit{C. Qu}, SIAM J. Math. Anal. 56, No. 2, 1672--1726 (2024; Zbl 07817074) Full Text: DOI
Huang, Jiaxi; Zhao, Lifeng Asymptotic behavior of incompressible Schrödinger flow for small data in three dimensions. (English) Zbl 07801722 J. Differ. Equations 386, 519-556 (2024). MSC: 35Q55 35Q41 35Q35 76D05 35P25 35B65 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{J. Huang} and \textit{L. Zhao}, J. Differ. Equations 386, 519--556 (2024; Zbl 07801722) Full Text: DOI arXiv
Perelman, Galina Formation of singularities in nonlinear dispersive PDEs. (English) Zbl 07823089 Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 5. Sections 9–11. Berlin: European Mathematical Society (EMS). 3854-3879 (2023). MSC: 35Q55 35Q41 35Q51 35A21 35B30 35B44 35C08 35A01 35A02 PDFBibTeX XMLCite \textit{G. Perelman}, in: International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6--14, 2022. Volume 5. Sections 9--11. Berlin: European Mathematical Society (EMS). 3854--3879 (2023; Zbl 07823089) Full Text: DOI OA License
Chen, Bo; Wang, Youde Smooth local solutions to Schrödinger flows with damping term for maps into symplectic manifolds. (English) Zbl 07787672 Pac. J. Math. 326, No. 2, 187-226 (2023). MSC: 35R01 35K51 35K58 35Q60 58J35 PDFBibTeX XMLCite \textit{B. Chen} and \textit{Y. Wang}, Pac. J. Math. 326, No. 2, 187--226 (2023; Zbl 07787672) Full Text: DOI
Herr, Sebastian; Kato, Isao; Kinoshita, Shinya; Spitz, Martin Local well-posedness of a system describing laser-plasma interactions. (English) Zbl 07785088 Vietnam J. Math. 51, No. 4, 759-770 (2023). MSC: 35Q55 35L70 35B30 35A01 35A02 PDFBibTeX XMLCite \textit{S. Herr} et al., Vietnam J. Math. 51, No. 4, 759--770 (2023; Zbl 07785088) Full Text: DOI arXiv OA License
Li, Ze Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: energy critical case. (English) Zbl 1528.35165 J. Eur. Math. Soc. (JEMS) 25, No. 12, 4879-4969 (2023). MSC: 35Q55 35Q41 35K05 53E30 35B65 35B40 35A01 35A02 35R01 PDFBibTeX XMLCite \textit{Z. Li}, J. Eur. Math. Soc. (JEMS) 25, No. 12, 4879--4969 (2023; Zbl 1528.35165) Full Text: DOI arXiv
Chen, Bo; Wang, Youde Very regular solution to Landau-Lifshitz-Gilbert system with spin-polarized transport. (English) Zbl 1528.35156 Front. Math. (Beijing) 18, No. 4, 751-795 (2023). MSC: 35Q55 35Q41 35Q60 78A60 82D40 35A01 35A02 35B65 35K59 35R09 PDFBibTeX XMLCite \textit{B. Chen} and \textit{Y. Wang}, Front. Math. (Beijing) 18, No. 4, 751--795 (2023; Zbl 1528.35156) Full Text: DOI arXiv
Lawrie, Andrew; Lührmann, Jonas; Oh, Sung-Jin; Shahshahani, Sohrab Asymptotic stability of harmonic maps on the hyperbolic plane under the Schrödinger maps evolution. (English) Zbl 07748334 Commun. Pure Appl. Math. 76, No. 3, 453-584 (2023). Reviewer: Alain Brillard (Riedisheim) MSC: 58J45 35B65 35Q41 35R01 PDFBibTeX XMLCite \textit{A. Lawrie} et al., Commun. Pure Appl. Math. 76, No. 3, 453--584 (2023; Zbl 07748334) Full Text: DOI arXiv
Ibrahim, Slim; Shimizu, Ikkei Phase transition threshold and stability of magnetic skyrmions. (English) Zbl 07732074 Commun. Math. Phys. 402, No. 3, 2627-2640 (2023). MSC: 35Q82 35Q60 82D40 82B26 78A30 35C08 35B38 PDFBibTeX XMLCite \textit{S. Ibrahim} and \textit{I. Shimizu}, Commun. Math. Phys. 402, No. 3, 2627--2640 (2023; Zbl 07732074) Full Text: DOI arXiv
Chen, Bo; Wang, Youde Existence and uniqueness of local regular solution to the Schrödinger flow from a bounded domain in \(\mathbb{R}^3\) into \(\mathbb{S}^2\). (English) Zbl 1518.35572 Commun. Math. Phys. 402, No. 1, 391-428 (2023). MSC: 35Q55 35Q41 35Q30 35Q31 35A01 35A02 35B65 35R09 82D40 35R01 PDFBibTeX XMLCite \textit{B. Chen} and \textit{Y. Wang}, Commun. Math. Phys. 402, No. 1, 391--428 (2023; Zbl 1518.35572) Full Text: DOI arXiv
Côte, Raphaël; Ignat, Radu Asymptotic stability of precessing domain walls for the Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction. (English) Zbl 07719636 Commun. Math. Phys. 401, No. 3, 2901-2957 (2023). MSC: 35Q82 35Q60 82D40 82D77 35B40 35B35 35B38 PDFBibTeX XMLCite \textit{R. Côte} and \textit{R. Ignat}, Commun. Math. Phys. 401, No. 3, 2901--2957 (2023; Zbl 07719636) Full Text: DOI arXiv
Fennell, James Equivariant heat and Schrödinger flows from Euclidean space to complex projective space. (English) Zbl 1515.35245 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 40, No. 2, 339-378 (2023). MSC: 35Q55 PDFBibTeX XMLCite \textit{J. Fennell}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 40, No. 2, 339--378 (2023; Zbl 1515.35245) Full Text: DOI arXiv
Wang, Guang-wu; Wang, You-de Global smooth solution to the incompressible Navier-Stokes-Landau-Lifshitz equations. (English) Zbl 1514.35366 Acta Math. Appl. Sin., Engl. Ser. 39, No. 1, 135-178 (2023). MSC: 35Q35 35Q30 35Q60 76D05 78A25 82D40 35B65 35A01 35A02 35B44 35L02 PDFBibTeX XMLCite \textit{G.-w. Wang} and \textit{Y.-d. Wang}, Acta Math. Appl. Sin., Engl. Ser. 39, No. 1, 135--178 (2023; Zbl 1514.35366) Full Text: DOI
Rong, Rong Partial regular solution to the coupled spin polarized system in three dimensions. (English) Zbl 1512.35567 Discrete Contin. Dyn. Syst., Ser. B 28, No. 8, 4293-4310 (2023). MSC: 35Q60 35Q56 82D40 35K59 35B65 35D30 PDFBibTeX XMLCite \textit{R. Rong}, Discrete Contin. Dyn. Syst., Ser. B 28, No. 8, 4293--4310 (2023; Zbl 1512.35567) Full Text: DOI
Zheng, Bowen On the blow-up solutions for the nonlinear radial Schrödinger equations with spatial variable coefficients. (English) Zbl 1508.35165 Osaka J. Math. 60, No. 1, 31-42 (2023). MSC: 35Q55 35Q41 35B44 35M11 37K10 PDFBibTeX XMLCite \textit{B. Zheng}, Osaka J. Math. 60, No. 1, 31--42 (2023; Zbl 1508.35165) Full Text: Link
Wang, Guangwu; Guo, Boling A blowup criterion to the strong solution to the multi-dimensional Landau-Lifshitz-Gilbert equation. (English) Zbl 1498.35116 Appl. Math. Lett. 135, Article ID 108410, 6 p. (2023). MSC: 35B44 35D35 35Q60 PDFBibTeX XMLCite \textit{G. Wang} and \textit{B. Guo}, Appl. Math. Lett. 135, Article ID 108410, 6 p. (2023; Zbl 1498.35116) Full Text: DOI
Song, Wenjing; Yang, Ganshan Vanishing Gilbert damping limit problem of Landau-Lifshitz-Gilbert equation. (English) Zbl 07815596 ZAMM, Z. Angew. Math. Mech. 102, No. 8, Article ID e202100136, 8 p. (2022). MSC: 35Q55 35Q60 78M30 82D40 37K15 PDFBibTeX XMLCite \textit{W. Song} and \textit{G. Yang}, ZAMM, Z. Angew. Math. Mech. 102, No. 8, Article ID e202100136, 8 p. (2022; Zbl 07815596) Full Text: DOI
Shimizu, Ikkei Local well-posedness of the Landau-Lifshitz equation with helicity term. (English) Zbl 1509.35297 J. Math. Phys. 63, No. 9, Article ID 091505, 27 p. (2022). MSC: 35Q60 82D40 35B45 35B65 PDFBibTeX XMLCite \textit{I. Shimizu}, J. Math. Phys. 63, No. 9, Article ID 091505, 27 p. (2022; Zbl 1509.35297) Full Text: DOI arXiv
Bai, Mengxue; Zhang, Jian Small multi solitons in a double power nonlinear Schrödinger equation. (English) Zbl 1496.35351 J. Differ. Equations 336, 239-274 (2022). MSC: 35Q55 35Q51 37K40 35C08 35B35 35J60 PDFBibTeX XMLCite \textit{M. Bai} and \textit{J. Zhang}, J. Differ. Equations 336, 239--274 (2022; Zbl 1496.35351) Full Text: DOI
de Laire, André Recent results for the Landau-Lifshitz equation. (English) Zbl 1490.35407 S\(\vec{\text{e}}\)MA J. 79, No. 2, 253-295 (2022). MSC: 35Q55 82D40 PDFBibTeX XMLCite \textit{A. de Laire}, S\(\vec{\text{e}}\)MA J. 79, No. 2, 253--295 (2022; Zbl 1490.35407) Full Text: DOI arXiv
Li, Ze On global dynamics of Schrödinger map flows on hyperbolic planes near harmonic maps. (English) Zbl 1491.35048 Commun. Math. Phys. 393, No. 1, 279-345 (2022). MSC: 35B40 35Q41 35R01 58J35 PDFBibTeX XMLCite \textit{Z. Li}, Commun. Math. Phys. 393, No. 1, 279--345 (2022; Zbl 1491.35048) Full Text: DOI arXiv
Deng, Haiyun; Liu, Hui; Song, Wenjing Finite difference scheme for the nonhomogeneous initial boundary value problem of critical Schrödinger map. (Chinese. English summary) Zbl 1513.65280 Acta Math. Sci., Ser. A, Chin. Ed. 41, No. 5, 1311-1322 (2021). MSC: 65M06 65M15 PDFBibTeX XMLCite \textit{H. Deng} et al., Acta Math. Sci., Ser. A, Chin. Ed. 41, No. 5, 1311--1322 (2021; Zbl 1513.65280) Full Text: Link
Liu, Hsiao-Fan; Terng, Chuu-Lian; Wu, Zhiwei Solitons for the Schrödinger flows on Hermitian symmetric spaces. (English) Zbl 1495.53073 Int. J. Math. 32, No. 12, Article ID 2140013, 29 p. (2021). Reviewer: Boris S. Kruglikov (Tromsø) MSC: 53C35 53E30 53E40 35C08 37K10 35Q55 PDFBibTeX XMLCite \textit{H.-F. Liu} et al., Int. J. Math. 32, No. 12, Article ID 2140013, 29 p. (2021; Zbl 1495.53073) Full Text: DOI
Neirameh, Ahmad Solitary wave solutions to the multidimensional Landau-Lifshitz equation. (English) Zbl 1478.35086 Adv. Math. Phys. 2021, Article ID 5538516, 7 p. (2021). MSC: 35C08 35Q60 PDFBibTeX XMLCite \textit{A. Neirameh}, Adv. Math. Phys. 2021, Article ID 5538516, 7 p. (2021; Zbl 1478.35086) Full Text: DOI
Zhong, Penghong; Chen, Ye; Yang, Ganshan The estimates of the ill-posedness index of the (deformed-) continuous Heisenberg spin equation. (English) Zbl 1483.35266 J. Math. Phys. 62, No. 10, Article ID 101510, 23 p. (2021). MSC: 35Q82 82C21 82D10 82D40 35C07 35C08 26A33 35R11 35R25 PDFBibTeX XMLCite \textit{P. Zhong} et al., J. Math. Phys. 62, No. 10, Article ID 101510, 23 p. (2021; Zbl 1483.35266) Full Text: DOI
Hirayama, Hiroyuki; Ikeda, Masahiro; Tanaka, Tomoyuki Well-posedness for the fourth-order Schrödinger equation with third order derivative nonlinearities. (English) Zbl 1481.35356 NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 5, Paper No. 46, 72 p. (2021). MSC: 35Q55 35Q41 35A01 35A02 35B45 35P25 37K10 PDFBibTeX XMLCite \textit{H. Hirayama} et al., NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 5, Paper No. 46, 72 p. (2021; Zbl 1481.35356) Full Text: DOI arXiv
Song, Chong Local existence and uniqueness of skew mean curvature flow. (English) Zbl 1472.53100 J. Reine Angew. Math. 776, 1-26 (2021). MSC: 53E10 76B47 35Q35 PDFBibTeX XMLCite \textit{C. Song}, J. Reine Angew. Math. 776, 1--26 (2021; Zbl 1472.53100) Full Text: DOI arXiv
Li, Ze Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: high dimensions. (English) Zbl 1472.35326 J. Funct. Anal. 281, No. 6, Article ID 109093, 76 p. (2021). MSC: 35Q41 35B65 32J27 35R01 PDFBibTeX XMLCite \textit{Z. Li}, J. Funct. Anal. 281, No. 6, Article ID 109093, 76 p. (2021; Zbl 1472.35326) Full Text: DOI arXiv
Huang, Jiaxi Local existence and uniqueness of Navier-Stokes-Schrödinger system. (English) Zbl 1464.35325 Commun. Math. Stat. 9, No. 1, 101-118 (2021). MSC: 35Q55 35B65 35B30 35Q35 35A01 35A02 PDFBibTeX XMLCite \textit{J. Huang}, Commun. Math. Stat. 9, No. 1, 101--118 (2021; Zbl 1464.35325) Full Text: DOI
Li, Qiaoxin; Guo, Boling; Liu, Fengxia; Liu, Wuming Weak and strong solutions to Landau-Lifshitz-Bloch-Maxwell equations with polarization. (English) Zbl 1467.35306 J. Differ. Equations 286, 47-83 (2021). MSC: 35Q60 78A25 82D40 35B65 35A01 35D30 35D35 PDFBibTeX XMLCite \textit{Q. Li} et al., J. Differ. Equations 286, 47--83 (2021; Zbl 1467.35306) Full Text: DOI
Grande, Ricardo; Kurianski, Kristin M.; Staffilani, Gigliola On the nonlinear Dysthe equation. (English) Zbl 1464.35224 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 207, Article ID 112292, 36 p. (2021). MSC: 35Q35 76B15 86A05 35B65 35B50 35C20 35A01 35A02 PDFBibTeX XMLCite \textit{R. Grande} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 207, Article ID 112292, 36 p. (2021; Zbl 1464.35224) Full Text: DOI arXiv
Li, Ze Global transversal stability of Euclidean planes under skew mean curvature flow evolutions. (English) Zbl 1467.53101 Calc. Var. Partial Differ. Equ. 60, No. 1, Paper No. 57, 20 p. (2021). MSC: 53E10 35Q35 PDFBibTeX XMLCite \textit{Z. Li}, Calc. Var. Partial Differ. Equ. 60, No. 1, Paper No. 57, 20 p. (2021; Zbl 1467.53101) Full Text: DOI arXiv
de Laire, André; Gravejat, Philippe The cubic Schrödinger regime of the Landau-Lifshitz equation with a strong easy-axis anisotropy. (English) Zbl 1462.35376 Rev. Mat. Iberoam. 37, No. 1, 95-128 (2021). MSC: 35Q60 35Q55 37K40 35C07 82D40 35B40 PDFBibTeX XMLCite \textit{A. de Laire} and \textit{P. Gravejat}, Rev. Mat. Iberoam. 37, No. 1, 95--128 (2021; Zbl 1462.35376) Full Text: DOI arXiv
Zhai, Jian; Zheng, Bo-Wen Global existence and blow-up solutions of the radial Schrödinger maps. (English) Zbl 1458.35360 Commun. Contemp. Math. 23, No. 2, Article ID 2050009, 22 p. (2021). MSC: 35Q40 35Q55 81Q05 35R09 35B44 35A01 35A02 PDFBibTeX XMLCite \textit{J. Zhai} and \textit{B.-W. Zheng}, Commun. Contemp. Math. 23, No. 2, Article ID 2050009, 22 p. (2021; Zbl 1458.35360) Full Text: DOI
Zhong, Penghong; Wu, Fengong; Tang, Shengxiang Renormalization for the Laplacian and global well-possness of the Landau-Lifshitz-Gilbert equation in dimensions \(n \geq 3\). (Renormalization for the Laplacian and global well-posedness of the Landau-Lifshitz-Gilbert equation in dimensions \(n \geq 3\).) (English) Zbl 1499.35325 Bound. Value Probl. 2020, Paper No. 96, 18 p. (2020). MSC: 35K45 35B30 35Q60 PDFBibTeX XMLCite \textit{P. Zhong} et al., Bound. Value Probl. 2020, Paper No. 96, 18 p. (2020; Zbl 1499.35325) Full Text: DOI
Herr, Sebastian; Lamm, Tobias; Schmid, Tobias; Schnaubelt, Roland Biharmonic wave maps: local wellposedness in high regularity. (English) Zbl 1481.35285 Nonlinearity 33, No. 5, 2270-2305 (2020). MSC: 35L76 35B65 35L30 PDFBibTeX XMLCite \textit{S. Herr} et al., Nonlinearity 33, No. 5, 2270--2305 (2020; Zbl 1481.35285) Full Text: DOI arXiv
Zhong, Penghong; Yang, Ganshan; Ma, Xuan Global existence of Landau-Lifshitz-Gilbert equation and self-similar blowup of harmonic map heat flow on \(\mathbb{S}^2\). (English) Zbl 1456.35067 Math. Comput. Simul. 174, 1-18 (2020). MSC: 35C06 35B44 58E20 53C43 PDFBibTeX XMLCite \textit{P. Zhong} et al., Math. Comput. Simul. 174, 1--18 (2020; Zbl 1456.35067) Full Text: DOI
Huang, Jiaxi; Wang, Youde; Zhao, Lifeng Equivariant Schrödinger map flow on two dimensional hyperbolic space. (English) Zbl 1435.35326 Discrete Contin. Dyn. Syst. 40, No. 7, 4379-4425 (2020). MSC: 35Q41 35B65 PDFBibTeX XMLCite \textit{J. Huang} et al., Discrete Contin. Dyn. Syst. 40, No. 7, 4379--4425 (2020; Zbl 1435.35326) Full Text: DOI
Pu, Xueke; Wang, Wendong Partial regularity to the Landau-Lifshitz equation with spin accumulation. (English) Zbl 1426.35059 J. Differ. Equations 268, No. 2, 707-737 (2020). MSC: 35B65 35Q60 58J35 35K59 PDFBibTeX XMLCite \textit{X. Pu} and \textit{W. Wang}, J. Differ. Equations 268, No. 2, 707--737 (2020; Zbl 1426.35059) Full Text: DOI arXiv
Herr, Sebastian Initial value problems for nonlinear dispersive equations at critical regularity. (English) Zbl 1446.35182 Baake, Michael (ed.) et al., Spectral structures and topological methods in mathematics. Zürich: European Mathematical Society (EMS). EMS Ser. Congr. Rep., 159-182 (2019). MSC: 35Q55 35Q41 35B65 35B40 PDFBibTeX XMLCite \textit{S. Herr}, in: Spectral structures and topological methods in mathematics. Zürich: European Mathematical Society (EMS). 159--182 (2019; Zbl 1446.35182) Full Text: DOI
Jia, Zonglin; Wang, Youde Global weak solutions to Landau-Lifshitz equations into compact Lie algebras. (English) Zbl 1441.35224 Front. Math. China 14, No. 6, 1163-1196 (2019). MSC: 35Q60 35D30 35G20 35G25 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{Y. Wang}, Front. Math. China 14, No. 6, 1163--1196 (2019; Zbl 1441.35224) Full Text: DOI arXiv
Xu, Xiuli; Pu, Xueke Global weak solutions of the Maxwell-Landau-Lifshitz equation with spin accumulation. (English) Zbl 1423.35173 Z. Angew. Math. Phys. 70, No. 5, Paper No. 137, 20 p. (2019). MSC: 35K51 35Q61 35Q60 82D40 PDFBibTeX XMLCite \textit{X. Xu} and \textit{X. Pu}, Z. Angew. Math. Phys. 70, No. 5, Paper No. 137, 20 p. (2019; Zbl 1423.35173) Full Text: DOI
Jia, Zong Lin; Wang, You De Local nonautonomous Schrödinger flows on Kähler manifolds. (English) Zbl 1425.53083 Acta Math. Sin., Engl. Ser. 35, No. 8, 1251-1299 (2019). MSC: 53C44 53C55 PDFBibTeX XMLCite \textit{Z. L. Jia} and \textit{Y. De Wang}, Acta Math. Sin., Engl. Ser. 35, No. 8, 1251--1299 (2019; Zbl 1425.53083) Full Text: DOI arXiv
Nahmod, Andrea R.; Staffilani, Gigliola Randomness and nonlinear evolution equations. (English) Zbl 1419.35255 Acta Math. Sin., Engl. Ser. 35, No. 6, 903-932 (2019). MSC: 35R35 35B10 35E15 35Q35 35Q55 35R60 PDFBibTeX XMLCite \textit{A. R. Nahmod} and \textit{G. Staffilani}, Acta Math. Sin., Engl. Ser. 35, No. 6, 903--932 (2019; Zbl 1419.35255) Full Text: DOI Link
Dodson, Benjamin; Lührmann, Jonas; Mendelson, Dana Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation. (English) Zbl 1428.35503 Adv. Math. 347, 619-676 (2019). Reviewer: Ayman Kachmar (Nabaṭiyya) MSC: 35Q55 35B40 35B25 35P25 35L05 35R60 PDFBibTeX XMLCite \textit{B. Dodson} et al., Adv. Math. 347, 619--676 (2019; Zbl 1428.35503) Full Text: DOI arXiv
Li, Ze; Zhao, Lifeng Convergence to harmonic maps for the Landau-Lifshitz flows between two dimensional hyperbolic spaces. (English) Zbl 1405.58008 Discrete Contin. Dyn. Syst. 39, No. 1, 607-638 (2019). MSC: 58J35 35K59 PDFBibTeX XMLCite \textit{Z. Li} and \textit{L. Zhao}, Discrete Contin. Dyn. Syst. 39, No. 1, 607--638 (2019; Zbl 1405.58008) Full Text: DOI arXiv
Candy, Timothy; Herr, Sebastian On the division problem for the wave maps equation. (English) Zbl 1411.35198 Ann. PDE 4, No. 2, Paper No. 17, 61 p. (2018). MSC: 35L52 35L15 PDFBibTeX XMLCite \textit{T. Candy} and \textit{S. Herr}, Ann. PDE 4, No. 2, Paper No. 17, 61 p. (2018; Zbl 1411.35198) Full Text: DOI arXiv
Zhong, Penghong; Zhang, Chao; Wu, Fengong Energy decay rate of multidimensional inhomogeneous Landau-Lifshitz-Gilbert equation and Schrödinger map equation on the sphere. (English) Zbl 1448.35490 Adv. Difference Equ. 2018, Paper No. 335, 25 p. (2018). MSC: 35Q56 35B44 PDFBibTeX XMLCite \textit{P. Zhong} et al., Adv. Difference Equ. 2018, Paper No. 335, 25 p. (2018; Zbl 1448.35490) Full Text: DOI
de Laire, André; Gravejat, Philippe The sine-Gordon regime of the Landau-Lifshitz equation with a strong easy-plane anisotropy. (English) Zbl 1418.35021 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, No. 7, 1885-1945 (2018). Reviewer: Denis Borisov (Ufa) MSC: 35B25 35A01 35Q55 35Q60 37K40 35L71 82D45 PDFBibTeX XMLCite \textit{A. de Laire} and \textit{P. Gravejat}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, No. 7, 1885--1945 (2018; Zbl 1418.35021) Full Text: DOI arXiv
Chang, Nai-Heng The Cauchy problem for a spin-liquid model in three space dimensions. (English) Zbl 1394.35468 Appl. Anal. 97, No. 10, 1771-1796 (2018). MSC: 35Q55 82D40 35A01 35A02 PDFBibTeX XMLCite \textit{N.-H. Chang}, Appl. Anal. 97, No. 10, 1771--1796 (2018; Zbl 1394.35468) Full Text: DOI
Pornnopparath, Donlapark Small data well-posedness for derivative nonlinear Schrödinger equations. (English) Zbl 1397.35290 J. Differ. Equations 265, No. 8, 3792-3840 (2018). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q55 35A01 35B45 PDFBibTeX XMLCite \textit{D. Pornnopparath}, J. Differ. Equations 265, No. 8, 3792--3840 (2018; Zbl 1397.35290) Full Text: DOI arXiv
Bahri, Yakine On the asymptotic stability in the energy space for multi-solitons of the Landau-Lifshitz equation. (English) Zbl 1391.35046 Trans. Am. Math. Soc. 370, No. 7, 4683-4707 (2018). MSC: 35B35 35B40 35Q51 35C08 35Q56 35C07 PDFBibTeX XMLCite \textit{Y. Bahri}, Trans. Am. Math. Soc. 370, No. 7, 4683--4707 (2018; Zbl 1391.35046) Full Text: DOI arXiv
Guo, ZiHua; Huang, ChunYan The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space. (English) Zbl 1394.35477 Sci. China, Math. 60, No. 11, 2155-2172 (2017). MSC: 35Q55 82D40 35Q60 35Q56 78A25 PDFBibTeX XMLCite \textit{Z. Guo} and \textit{C. Huang}, Sci. China, Math. 60, No. 11, 2155--2172 (2017; Zbl 1394.35477) Full Text: DOI arXiv
Li, Ze; Zhao, Lifeng Asymptotic behaviors of Landau-Lifshitz flows from \(\mathbb {R}^2\) to Kähler manifolds. (English) Zbl 1375.35045 Calc. Var. Partial Differ. Equ. 56, No. 4, Paper No. 96, 35 p. (2017). Reviewer: Eric Stachura (Haverford) MSC: 35B40 35Q82 58J35 58E50 PDFBibTeX XMLCite \textit{Z. Li} and \textit{L. Zhao}, Calc. Var. Partial Differ. Equ. 56, No. 4, Paper No. 96, 35 p. (2017; Zbl 1375.35045) Full Text: DOI arXiv
Zhong, Penghong; Yang, Ganshan Finite time blowup of multidimensional inhomogeneous isotropic Landau-Lifshitz equation on a hyperbolic space. (English) Zbl 1368.35257 Comput. Math. Appl. 73, No. 3, 433-449 (2017). MSC: 35Q60 35B44 35B40 PDFBibTeX XMLCite \textit{P. Zhong} and \textit{G. Yang}, Comput. Math. Appl. 73, No. 3, 433--449 (2017; Zbl 1368.35257) Full Text: DOI
De Laire, André; Gravejat, Philippe Stability of solitons of the Landau-Lifshitz equation with planar anisotropy. (English. French summary) Zbl 1355.35016 Sémin. Laurent Schwartz, EDP Appl. 2014-2015, Exp. No. 17, 27 p (2016). MSC: 35B35 35Q60 35C08 PDFBibTeX XMLCite \textit{A. De Laire} and \textit{P. Gravejat}, Sémin. Laurent Schwartz, EDP Appl. 2014--2015, Exp. No. 17, 27 p (2016; Zbl 1355.35016) Full Text: DOI
Bejenaru, Ioan; Ionescu, Alexandru; Kenig, Carlos; Tataru, Daniel Equivariant Schrödinger maps in two spatial dimensions: the \(\mathbb{H}^2\) target. (English) Zbl 1370.35235 Kyoto J. Math. 56, No. 2, 283-323 (2016). MSC: 35Q41 35B65 PDFBibTeX XMLCite \textit{I. Bejenaru} et al., Kyoto J. Math. 56, No. 2, 283--323 (2016; Zbl 1370.35235) Full Text: DOI arXiv Euclid
Bejenaru, Ioan; Herr, Sebastian The cubic Dirac equation: small initial data in \({H^{\frac{1}{2}}(\mathbb R^2)}\). (English) Zbl 1339.35261 Commun. Math. Phys. 343, No. 2, 515-562 (2016). MSC: 35Q41 35Q53 35B45 PDFBibTeX XMLCite \textit{I. Bejenaru} and \textit{S. Herr}, Commun. Math. Phys. 343, No. 2, 515--562 (2016; Zbl 1339.35261) Full Text: DOI arXiv
Fan, Jishan; Ozawa, Tohru A regularity criterion for the Schrödinger map. (English) Zbl 1327.35290 Mityushev, Vladimir V. (ed.) et al., Current trends in analysis and its applications. Proceedings of the 9th ISAAC congress, Kraków, Poland, August 5–9, 2013. Cham: Birkhäuser/Springer (ISBN 978-3-319-12576-3/pbk; 978-3-319-12577-0/ebook). Trends in Mathematics. Research Perspectives, 217-223 (2015). MSC: 35Q05 35Q35 PDFBibTeX XMLCite \textit{J. Fan} and \textit{T. Ozawa}, in: Current trends in analysis and its applications. Proceedings of the 9th ISAAC congress, Kraków, Poland, August 5--9, 2013. Cham: Birkhäuser/Springer. 217--223 (2015; Zbl 1327.35290) Full Text: DOI
Lin, Junyu; Lai, Baishun; Wang, Changyou Global well-posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey spaces. (English) Zbl 1328.35081 Calc. Var. Partial Differ. Equ. 54, No. 1, 665-692 (2015). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 35K55 35Q56 PDFBibTeX XMLCite \textit{J. Lin} et al., Calc. Var. Partial Differ. Equ. 54, No. 1, 665--692 (2015; Zbl 1328.35081) Full Text: DOI arXiv
Dodson, Benjamin; Smith, Paul A controlling norm for energy-critical Schrödinger maps. (English) Zbl 1328.35210 Trans. Am. Math. Soc. 367, No. 10, 7193-7220 (2015). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35B33 PDFBibTeX XMLCite \textit{B. Dodson} and \textit{P. Smith}, Trans. Am. Math. Soc. 367, No. 10, 7193--7220 (2015; Zbl 1328.35210) Full Text: DOI arXiv
Chemin, Jean-Yves; Salort, Delphine Wellposedness of some quasi-linear Schrödinger equations. (English) Zbl 1333.35225 Sci. China, Math. 58, No. 5, 891-914 (2015). Reviewer: Natalia Bondarenko (Saratov) MSC: 35Q41 35S50 35Q55 35B45 PDFBibTeX XMLCite \textit{J.-Y. Chemin} and \textit{D. Salort}, Sci. China, Math. 58, No. 5, 891--914 (2015; Zbl 1333.35225) Full Text: DOI
Oh, Sung-Jin Finite energy global well-posedness of the Yang-Mills equations on \(\mathbb{R}^{1+3}\): an approach using the Yang-Mills heat flow. (English) Zbl 1325.35180 Duke Math. J. 164, No. 9, 1669-1732 (2015). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q40 70S15 81T13 35Q60 PDFBibTeX XMLCite \textit{S.-J. Oh}, Duke Math. J. 164, No. 9, 1669--1732 (2015; Zbl 1325.35180) Full Text: DOI arXiv Euclid
Chousionis, Vasilis; Erdoğan, M. Burak; Tzirakis, Nikolaos Fractal solutions of linear and nonlinear dispersive partial differential equations. (English) Zbl 1317.35230 Proc. Lond. Math. Soc. (3) 110, No. 3, 543-564 (2015). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35Q53 35R11 PDFBibTeX XMLCite \textit{V. Chousionis} et al., Proc. Lond. Math. Soc. (3) 110, No. 3, 543--564 (2015; Zbl 1317.35230) Full Text: DOI arXiv
Bejenaru, Ioan; Herr, Sebastian The cubic Dirac equation: small initial data in \(H^1(\mathbb R^3)\). (English) Zbl 1321.35180 Commun. Math. Phys. 335, No. 1, 43-82 (2015). Reviewer: Miguel A. Alejo (Florianópolis) MSC: 35Q41 35B45 35Q53 PDFBibTeX XMLCite \textit{I. Bejenaru} and \textit{S. Herr}, Commun. Math. Phys. 335, No. 1, 43--82 (2015; Zbl 1321.35180) Full Text: DOI arXiv
Sun, Xiaowei; Wang, Youde New geometric flows on Riemannian manifolds and applications to Schrödinger-Airy flows. (English) Zbl 1311.58019 Sci. China, Math. 57, No. 11, 2247-2272 (2014). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J60 53C44 35Q53 PDFBibTeX XMLCite \textit{X. Sun} and \textit{Y. Wang}, Sci. China, Math. 57, No. 11, 2247--2272 (2014; Zbl 1311.58019) Full Text: DOI arXiv
Bejenaru, Ioan; Tataru, Daniel Near soliton evolution for equivariant Schrödinger maps in two spatial dimensions. (English) Zbl 1303.58009 Mem. Am. Math. Soc. 1069, v, 108 p. (2014). Reviewer: Dian K. Palagachev (Bari) MSC: 58J35 35B65 35K45 35C08 PDFBibTeX XMLCite \textit{I. Bejenaru} and \textit{D. Tataru}, Near soliton evolution for equivariant Schrödinger maps in two spatial dimensions. Providence, RI: American Mathematical Society (AMS) (2014; Zbl 1303.58009) Full Text: DOI arXiv
Perelman, Galina Blow up dynamics for equivariant critical Schrödinger maps. (English) Zbl 1300.35008 Commun. Math. Phys. 330, No. 1, 69-105 (2014). Reviewer: Dian K. Palagachev (Bari) MSC: 35J10 35B44 PDFBibTeX XMLCite \textit{G. Perelman}, Commun. Math. Phys. 330, No. 1, 69--105 (2014; Zbl 1300.35008) Full Text: DOI arXiv
Smith, Paul An unconstrained Lagrangian formulation and conservation laws for the Schrödinger map system. (English) Zbl 1348.58021 J. Math. Phys. 55, No. 5, 051502, 16 p. (2014). MSC: 58J70 PDFBibTeX XMLCite \textit{P. Smith}, J. Math. Phys. 55, No. 5, 051502, 16 p. (2014; Zbl 1348.58021) Full Text: DOI arXiv
Oh, Sung-Jin Gauge choice for the Yang-Mills equations using the Yang-Mills heat flow and local well-posedness in \(H^{1}\). (English) Zbl 1295.35328 J. Hyperbolic Differ. Equ. 11, No. 1, 1-108 (2014). Reviewer: Ahmed Lesfari (El Jadida) MSC: 35L71 70S15 PDFBibTeX XMLCite \textit{S.-J. Oh}, J. Hyperbolic Differ. Equ. 11, No. 1, 1--108 (2014; Zbl 1295.35328) Full Text: DOI arXiv
Song, Chong; Sun, Xiaowei; Wang, Youde Geometric solitons of Hamiltonian flows on manifolds. (English) Zbl 1337.37056 J. Math. Phys. 54, No. 12, 121505, 17 p. (2013). MSC: 37K10 37K40 37K25 35C08 PDFBibTeX XMLCite \textit{C. Song} et al., J. Math. Phys. 54, No. 12, 121505, 17 p. (2013; Zbl 1337.37056) Full Text: DOI arXiv
Wang, Baoxiang Globally well and ill posedness for non-elliptic derivative Schrödinger equations with small rough data. (English) Zbl 1348.35248 J. Funct. Anal. 265, No. 12, 3009-3052 (2013). MSC: 35Q55 35B45 47N20 47D08 PDFBibTeX XMLCite \textit{B. Wang}, J. Funct. Anal. 265, No. 12, 3009--3052 (2013; Zbl 1348.35248) Full Text: DOI arXiv
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. (English) Zbl 1326.35052 Invent. Math. 193, No. 2, 249-365 (2013). Reviewer: Guanggan Chen (Chengdu) MSC: 35B44 35Q55 PDFBibTeX XMLCite \textit{F. Merle} et al., Invent. Math. 193, No. 2, 249--365 (2013; Zbl 1326.35052) Full Text: DOI arXiv
Zhong, Penghong; Wang, Shu; Zeng, Ming Some exact blowup solutions to multidimensional Schrödinger map equation on hyperbolic space and cone. (English) Zbl 1268.35019 Mod. Phys. Lett. A 28, No. 10, Article ID 1350043 (2013). MSC: 35B44 35J10 81Q05 PDFBibTeX XMLCite \textit{P. Zhong} et al., Mod. Phys. Lett. A 28, No. 10, Article ID 1350043 (2013; Zbl 1268.35019) Full Text: DOI
Sun, Xiao Wei; Wang, You De Geometric Schrödinger-Airy flows on Kähler manifolds. (English) Zbl 1266.58020 Acta Math. Sin., Engl. Ser. 29, No. 2, 209-240 (2013). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J60 35Q55 35Q53 53C55 PDFBibTeX XMLCite \textit{X. W. Sun} and \textit{Y. De Wang}, Acta Math. Sin., Engl. Ser. 29, No. 2, 209--240 (2013; Zbl 1266.58020) Full Text: DOI arXiv
Fan, Jishan; Ozawa, Tohru Regularity criteria for hyperbolic Navier-Stokes and related system. (English) Zbl 1254.35042 ISRN Math. Anal. 2012, Article ID 796368, 7 p. (2012). MSC: 35B65 35Q30 46E35 76D05 PDFBibTeX XMLCite \textit{J. Fan} and \textit{T. Ozawa}, ISRN Math. Anal. 2012, Article ID 796368, 7 p. (2012; Zbl 1254.35042) Full Text: DOI
Wang, Yuzhao Local well-posedness for hyperbolic-elliptic Ishimori equation. (English) Zbl 1242.35181 J. Differ. Equations 252, No. 9, 4625-4655 (2012). MSC: 35M33 35B30 PDFBibTeX XMLCite \textit{Y. Wang}, J. Differ. Equations 252, No. 9, 4625--4655 (2012; Zbl 1242.35181) Full Text: DOI arXiv
Song, Chong; Wang, You De Schrödinger soliton from Lorentzian manifolds. (English) Zbl 1364.37150 Acta Math. Sin., Engl. Ser. 27, No. 8, 1455-1476 (2011). MSC: 37K40 58J60 35L70 37K25 PDFBibTeX XMLCite \textit{C. Song} and \textit{Y. De Wang}, Acta Math. Sin., Engl. Ser. 27, No. 8, 1455--1476 (2011; Zbl 1364.37150) Full Text: DOI arXiv
Wang, Yuzhao Global well-posedness and scattering for derivative Schrödinger equation. (English) Zbl 1229.35277 Commun. Partial Differ. Equations 36, No. 10-12, 1694-1722 (2011). MSC: 35Q55 42B37 PDFBibTeX XMLCite \textit{Y. Wang}, Commun. Partial Differ. Equations 36, No. 10--12, 1694--1722 (2011; Zbl 1229.35277) Full Text: DOI arXiv
Merle, Frank; Raphaël, Pierre; Rodnianski, Igor Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. (Dynamique explosive de solutions régulières équivariantes de l’application de Schrödinger map.) (English. Abridged French version) Zbl 1213.35139 C. R., Math., Acad. Sci. Paris 349, No. 5-6, 279-283 (2011). MSC: 35B44 35K59 35K15 PDFBibTeX XMLCite \textit{F. Merle} et al., C. R., Math., Acad. Sci. Paris 349, No. 5--6, 279--283 (2011; Zbl 1213.35139) Full Text: DOI arXiv
Bejenaru, I.; Ionescu, A. D.; Kenig, C. E. On the stability of certain spin models in \(2+1\) dimensions. (English) Zbl 1215.35145 J. Geom. Anal. 21, No. 1, 1-39 (2011). Reviewer: Bernard Ducomet (Bruyères le Châtel) MSC: 35Q55 81Q05 PDFBibTeX XMLCite \textit{I. Bejenaru} et al., J. Geom. Anal. 21, No. 1, 1--39 (2011; Zbl 1215.35145) Full Text: DOI arXiv
Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schrödinger maps on \(\mathbb R^2\). (English) Zbl 1205.35294 Commun. Math. Phys. 300, No. 1, 205-242 (2010). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q55 35Q60 82D40 35B45 35B35 35B05 80A20 PDFBibTeX XMLCite \textit{S. Gustafson} et al., Commun. Math. Phys. 300, No. 1, 205--242 (2010; Zbl 1205.35294) Full Text: DOI arXiv
Germain, Pierre; Shatah, Jalal; Zeng, Chongchun Self-similar solutions for the Schrödinger map equation. (English) Zbl 1186.35200 Math. Z. 264, No. 3, 697-707 (2010). MSC: 35Q55 35B40 35B44 81Q05 58J90 35B65 PDFBibTeX XMLCite \textit{P. Germain} et al., Math. Z. 264, No. 3, 697--707 (2010; Zbl 1186.35200) Full Text: DOI