Ye, Zhuan Global well-posedness for a model of 2D temperature-dependent Boussinesq equations without diffusivity. (English) Zbl 07283577 J. Differ. Equations 271, 107-127 (2021). MSC: 35Q35 35B65 76D03 35B65 35A01 35A02 PDF BibTeX XML Cite \textit{Z. Ye}, J. Differ. Equations 271, 107--127 (2021; Zbl 07283577) Full Text: DOI
Ju, Luman On the profiles of locally self-similar solutions for the 2D inviscid Boussinesq equations. (English) Zbl 1433.35282 J. Math. Anal. Appl. 484, No. 1, Article ID 123671, 31 p. (2020). MSC: 35Q35 35C06 35B44 35B40 35Q31 76R10 PDF BibTeX XML Cite \textit{L. Ju}, J. Math. Anal. Appl. 484, No. 1, Article ID 123671, 31 p. (2020; Zbl 1433.35282) Full Text: DOI
Tao, Lizheng; Wu, Jiahong The 2D Boussinesq equations with vertical dissipation and linear stability of shear flows. (English) Zbl 1416.35218 J. Differ. Equations 267, No. 3, 1731-1747 (2019). MSC: 35Q35 76F10 35B35 PDF BibTeX XML Cite \textit{L. Tao} and \textit{J. Wu}, J. Differ. Equations 267, No. 3, 1731--1747 (2019; Zbl 1416.35218) Full Text: DOI
Ye, Zhuan Some new regularity criteria for the 2D Euler-Boussinesq equations via the temperature. (English) Zbl 1409.35175 Acta Appl. Math. 157, No. 1, 141-169 (2018). MSC: 35Q35 35B65 76D03 PDF BibTeX XML Cite \textit{Z. Ye}, Acta Appl. Math. 157, No. 1, 141--169 (2018; Zbl 1409.35175) Full Text: DOI
Meddour, H.; Zerguine, M. Optimal rate of convergence in stratified Boussinesq system. (English) Zbl 1404.35366 Dyn. Partial Differ. Equ. 15, No. 4, 235-263 (2018). MSC: 35Q35 35B65 76D05 PDF BibTeX XML Cite \textit{H. Meddour} and \textit{M. Zerguine}, Dyn. Partial Differ. Equ. 15, No. 4, 235--263 (2018; Zbl 1404.35366) Full Text: DOI
Doering, Charles R.; Wu, Jiahong; Zhao, Kun; Zheng, Xiaoming Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion. (English) Zbl 1398.35164 Physica D 376-377, 144-159 (2018). MSC: 35Q35 35A01 35B20 35C05 65M60 PDF BibTeX XML Cite \textit{C. R. Doering} et al., Physica D 376--377, 144--159 (2018; Zbl 1398.35164) Full Text: DOI
Ye, Zhuan On the improved blow-up criterion for the 2D zero diffusivity Boussinesq equations with temperature-dependent viscosity. (English) Zbl 1398.35184 Appl. Anal. 97, No. 12, 2037-2058 (2018). MSC: 35Q35 35B65 76D03 35B44 PDF BibTeX XML Cite \textit{Z. Ye}, Appl. Anal. 97, No. 12, 2037--2058 (2018; Zbl 1398.35184) Full Text: DOI
Wu, Jiahong; Xu, Xiaojing; Ye, Zhuan The 2D Boussinesq equations with fractional horizontal dissipation and thermal diffusion. (English. French summary) Zbl 1392.35240 J. Math. Pures Appl. (9) 115, 187-217 (2018). MSC: 35Q35 35B65 76D03 35B45 35R11 PDF BibTeX XML Cite \textit{J. Wu} et al., J. Math. Pures Appl. (9) 115, 187--217 (2018; Zbl 1392.35240) Full Text: DOI
Fang, Daoyuan; Le, Wenjun; Zhang, Ting The 2D regularized incompressible Boussinesq equations with general critical dissipations. (English) Zbl 1390.35268 J. Math. Anal. Appl. 461, No. 1, 868-915 (2018). MSC: 35Q35 26A33 35B65 76D05 35A01 35A02 PDF BibTeX XML Cite \textit{D. Fang} et al., J. Math. Anal. Appl. 461, No. 1, 868--915 (2018; Zbl 1390.35268) Full Text: DOI
Quintero, José Raúl; Muñoz Grajales, Juan Carlos On the existence and computation of periodic travelling waves for a 2D water wave model. (English) Zbl 1387.35093 Commun. Pure Appl. Anal. 17, No. 2, 557-578 (2018). MSC: 35C07 35C08 65M70 35A15 35A24 35B10 PDF BibTeX XML Cite \textit{J. R. Quintero} and \textit{J. C. Muñoz Grajales}, Commun. Pure Appl. Anal. 17, No. 2, 557--578 (2018; Zbl 1387.35093) Full Text: DOI
Ye, Zhuan Global smooth solution to the 2D Boussinesq equations with fractional dissipation. (English) Zbl 1369.35072 Math. Methods Appl. Sci. 40, No. 12, 4595-4612 (2017). MSC: 35Q35 35B65 76D03 PDF BibTeX XML Cite \textit{Z. Ye}, Math. Methods Appl. Sci. 40, No. 12, 4595--4612 (2017; Zbl 1369.35072) Full Text: DOI arXiv
Ye, Zhuan; Xu, Xiaojing; Xue, Liutang On the global regularity of the 2D Boussinesq equations with fractional dissipation. (English) Zbl 1372.35254 Math. Nachr. 290, No. 8-9, 1420-1439 (2017). MSC: 35Q35 35B65 76D03 35R11 PDF BibTeX XML Cite \textit{Z. Ye} et al., Math. Nachr. 290, No. 8--9, 1420--1439 (2017; Zbl 1372.35254) Full Text: DOI
Hu, Weiwei; Kukavica, Igor; Wang, Fei; Ziane, Mohammed Boussinesq equations with zero viscosity or zero diffusivity: a review. (English) Zbl 1362.35231 Robinson, James C. (ed.) et al., Recent progress in the theory of the Euler and Navier-Stokes equations. Based on the workshop “The Navier-Stokes equations in Venice”, Venice, Italy, April 8–12, 2013. Cambridge: Cambridge University Press (ISBN 978-1-107-55497-9/pbk; 978-1-316-40710-3/ebook). London Mathematical Society Lecture Note Series 430, 77-95 (2016). MSC: 35Q35 35A01 35B65 PDF BibTeX XML Cite \textit{W. Hu} et al., Lond. Math. Soc. Lect. Note Ser. 430, 77--95 (2016; Zbl 1362.35231)
Ye, Zhuan Remarks on the improved regularity criterion for the 2D Euler-Boussinesq equations with supercritical dissipation. (English) Zbl 1358.35139 Z. Angew. Math. Phys. 67, No. 6, Article ID 149, 18 p. (2016). MSC: 35Q35 35B65 76D03 42B25 PDF BibTeX XML Cite \textit{Z. Ye}, Z. Angew. Math. Phys. 67, No. 6, Article ID 149, 18 p. (2016; Zbl 1358.35139) Full Text: DOI
Wu, Jiahong; Xu, Xiaojing; Xue, Liutang; Ye, Zhuan Regularity results for the 2D Boussinesq equations with critical or supercritical dissipation. (English) Zbl 1358.35136 Commun. Math. Sci. 14, No. 7, 1963-1997 (2016). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q35 35B65 76D03 PDF BibTeX XML Cite \textit{J. Wu} et al., Commun. Math. Sci. 14, No. 7, 1963--1997 (2016; Zbl 1358.35136) Full Text: DOI
Ye, Zhuan A note on global regularity results for 2D Boussinesq equations with fractional dissipation. (English) Zbl 1358.35138 Ann. Pol. Math. 117, No. 3, 231-247 (2016). MSC: 35Q35 35B65 76D03 26A33 PDF BibTeX XML Cite \textit{Z. Ye}, Ann. Pol. Math. 117, No. 3, 231--247 (2016; Zbl 1358.35138) Full Text: DOI arXiv
Wu, Jiahong The 2D Boussinesq equations with partial or fractional dissipation. (English) Zbl 1348.35204 Chemin, Jean-Yves (ed.) et al., Lectures on the analysis of nonlinear partial differential equations. Part 4. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-317-3/pbk). Morningside Lectures in Mathematics 4, 223-269 (2016). MSC: 35Q35 35-02 76D05 26A33 86A05 86A10 PDF BibTeX XML Cite \textit{J. Wu}, Morningside Lect. Math. 4, 223--269 (2016; Zbl 1348.35204)
Qian, Chenyin Blow-up criterion for the 2D Euler-Boussinesq system in terms of temperature. (English) Zbl 1343.35196 Electron. J. Differ. Equ. 2016, Paper No. 73, 11 p. (2016). MSC: 35Q35 76D05 35B44 26A33 PDF BibTeX XML Cite \textit{C. Qian}, Electron. J. Differ. Equ. 2016, Paper No. 73, 11 p. (2016; Zbl 1343.35196) Full Text: EMIS
Ye, Zhuan; Xu, Xiaojing Global regularity results of the 2D Boussinesq equations with fractional Laplacian dissipation. (English) Zbl 1346.35168 J. Math. Fluid Mech. 18, No. 2, 361-380 (2016). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q35 35B65 76D03 26A33 42B25 PDF BibTeX XML Cite \textit{Z. Ye} and \textit{X. Xu}, J. Math. Fluid Mech. 18, No. 2, 361--380 (2016; Zbl 1346.35168) Full Text: DOI arXiv
Ye, Zhuan On the regularity criterion for the 2D Boussinesq equations involving the temperature. (English) Zbl 1335.35207 Appl. Anal. 95, No. 3, 615-626 (2016). MSC: 35Q35 35B65 76D03 26A33 PDF BibTeX XML Cite \textit{Z. Ye}, Appl. Anal. 95, No. 3, 615--626 (2016; Zbl 1335.35207) Full Text: DOI
Ye, Zhuan; Xu, Xiaojing Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation. (English) Zbl 1341.35135 J. Differ. Equations 260, No. 8, 6716-6744 (2016). Reviewer: Bernard Ducomet (Bruyères le Châtel) MSC: 35Q35 35B65 76D03 26A33 PDF BibTeX XML Cite \textit{Z. Ye} and \textit{X. Xu}, J. Differ. Equations 260, No. 8, 6716--6744 (2016; Zbl 1341.35135) Full Text: DOI
Fang, Daoyuan; Qian, Chenyin; Zhang, Ting Global well-posedness for 2D Boussinesq system with general supercritical dissipation. (English) Zbl 1338.35359 Nonlinear Anal., Real World Appl. 27, 326-349 (2016). Reviewer: Marin I. Marin (Braşov) MSC: 35Q35 35B44 35S30 49K40 86A05 PDF BibTeX XML Cite \textit{D. Fang} et al., Nonlinear Anal., Real World Appl. 27, 326--349 (2016; Zbl 1338.35359) Full Text: DOI
Jia, Junxiong; Peng, Jigen; Li, Kexue On the global well-posedness of a generalized 2D Boussinesq equations. (English) Zbl 1327.76048 NoDEA, Nonlinear Differ. Equ. Appl. 22, No. 4, 911-945 (2015). MSC: 76D03 76D05 PDF BibTeX XML Cite \textit{J. Jia} et al., NoDEA, Nonlinear Differ. Equ. Appl. 22, No. 4, 911--945 (2015; Zbl 1327.76048) Full Text: DOI arXiv
Ye, Zhuan; Xu, Xiaojing Remarks on global regularity of the 2D Boussinesq equations with fractional dissipation. (English) Zbl 1405.35171 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 125, 715-724 (2015). MSC: 35Q35 35B65 76D03 PDF BibTeX XML Cite \textit{Z. Ye} and \textit{X. Xu}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 125, 715--724 (2015; Zbl 1405.35171) Full Text: DOI
Jiu, Quansen; Wu, Jiahong; Yang, Wanrong Eventual regularity of the two-dimensional Boussinesq equations with supercritical dissipation. (English) Zbl 1311.35221 J. Nonlinear Sci. 25, No. 1, 37-58 (2015). MSC: 35Q35 76D03 35B65 35D30 26A33 PDF BibTeX XML Cite \textit{Q. Jiu} et al., J. Nonlinear Sci. 25, No. 1, 37--58 (2015; Zbl 1311.35221) Full Text: DOI
Chae, Dongho; Constantin, Peter; Wu, Jiahong An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations. (English) Zbl 1307.35213 J. Math. Fluid Mech. 16, No. 3, 473-480 (2014); erratum ibid. 16, No. 3, 481 (2014). MSC: 35Q35 76D03 PDF BibTeX XML Cite \textit{D. Chae} et al., J. Math. Fluid Mech. 16, No. 3, 473--480 (2014; Zbl 1307.35213) Full Text: DOI arXiv
Yang, Wanrong; Jiu, Quansen; Wu, Jiahong Global well-posedness for a class of 2D Boussinesq systems with fractional dissipation. (English) Zbl 1300.35108 J. Differ. Equations 257, No. 11, 4188-4213 (2014). MSC: 35Q35 76D03 35B65 26A33 35R11 PDF BibTeX XML Cite \textit{W. Yang} et al., J. Differ. Equations 257, No. 11, 4188--4213 (2014; Zbl 1300.35108) Full Text: DOI
Chueshov, Igor; Shcherbina, Alexey Semi-weak well-posedness and attractors for 2D Schrödinger-Boussinesq equations. (English) Zbl 1282.35320 Evol. Equ. Control Theory 1, No. 1, 57-80 (2012). MSC: 35Q40 35B40 37L05 37L30 PDF BibTeX XML Cite \textit{I. Chueshov} and \textit{A. Shcherbina}, Evol. Equ. Control Theory 1, No. 1, 57--80 (2012; Zbl 1282.35320) Full Text: DOI
Farah, Luiz Gustavo; Rousset, Frederic; Tzvetkov, Nikolay Oscillatory integral estimates and global well-posedness for the 2D Boussinesq equation. (English) Zbl 1257.35164 Bull. Braz. Math. Soc. (N.S.) 43, No. 4, 655-679 (2012). MSC: 35Q53 35B30 35B05 PDF BibTeX XML Cite \textit{L. G. Farah} et al., Bull. Braz. Math. Soc. (N.S.) 43, No. 4, 655--679 (2012; Zbl 1257.35164) Full Text: DOI
Wu, Gang; Xue, Liutang Global well-posedness for the 2D inviscid Bénard system with fractional diffusivity and Yudovich’s type data. (English) Zbl 1305.35119 J. Differ. Equations 253, No. 1, 100-125 (2012). MSC: 35Q35 35B30 35Q86 35R11 76B03 PDF BibTeX XML Cite \textit{G. Wu} and \textit{L. Xue}, J. Differ. Equations 253, No. 1, 100--125 (2012; Zbl 1305.35119) Full Text: DOI
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong Global regularity results for the 2D Boussinesq equations with vertical dissipation. (English) Zbl 1232.35111 J. Differ. Equations 251, No. 6, 1637-1655 (2011). Reviewer: A. D. Osborne (Keele) MSC: 35Q30 35B45 35B65 76D03 76D09 35A01 35A02 PDF BibTeX XML Cite \textit{D. Adhikari} et al., J. Differ. Equations 251, No. 6, 1637--1655 (2011; Zbl 1232.35111) Full Text: DOI
Zhao, Kun Global regularity for a coupled Cahn-Hilliard-Boussinesq system on bounded domains. (English) Zbl 1219.35199 Q. Appl. Math. 69, No. 2, 331-356 (2011). MSC: 35Q35 35B65 35B40 PDF BibTeX XML Cite \textit{K. Zhao}, Q. Appl. Math. 69, No. 2, 331--356 (2011; Zbl 1219.35199) Full Text: DOI Link
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong The 2D Boussinesq equations with vertical viscosity and vertical diffusivity. (English) Zbl 1193.35144 J. Differ. Equations 249, No. 5, 1078-1088 (2010). MSC: 35Q35 35B65 76D03 76R50 PDF BibTeX XML Cite \textit{D. Adhikari} et al., J. Differ. Equations 249, No. 5, 1078--1088 (2010; Zbl 1193.35144) Full Text: DOI
Beneš, L.; Fürst, J.; Fraunié, Ph. Numerical simulation of the towing tank problem using high order schemes. (English) Zbl 1400.76023 Hegarty, Alan F. (ed.) et al., BAIL 2008 – Boundary and interior layers. Proceedings of the international conference on boundary and interior layers – computational and asymptotic methods, Limerick, Ireland, July 28–August 1, 2008. Berlin: Springer (ISBN 978-3-642-00604-3/pbk; 978-3-642-00605-0/ebook). Lecture Notes in Computational Science and Engineering 69, 79-93 (2009). MSC: 76D05 76M25 PDF BibTeX XML Cite \textit{L. Beneš} et al., Lect. Notes Comput. Sci. Eng. 69, 79--93 (2009; Zbl 1400.76023) Full Text: DOI
Abidi, H.; Hmidi, T. On the global well-posedness for Boussinesq system. (English) Zbl 1111.35032 J. Differ. Equations 233, No. 1, 199-220 (2007). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35Q30 76D03 76D05 PDF BibTeX XML Cite \textit{H. Abidi} and \textit{T. Hmidi}, J. Differ. Equations 233, No. 1, 199--220 (2007; Zbl 1111.35032) Full Text: DOI
Chueshov, Igor; Lasiecka, Irena Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models. (English) Zbl 1220.35014 Discrete Contin. Dyn. Syst. 15, No. 3, 777-809 (2006). Reviewer: Michael Scheutzow (Berlin) MSC: 35B41 47H10 34D35 60H25 35G25 PDF BibTeX XML Cite \textit{I. Chueshov} and \textit{I. Lasiecka}, Discrete Contin. Dyn. Syst. 15, No. 3, 777--809 (2006; Zbl 1220.35014) Full Text: DOI
You, Yuncheng Global dynamics of 2D Boussinesq equations. (English) Zbl 0927.37058 Nonlinear Anal., Theory Methods Appl. 30, No. 7, 4643-4654 (1997). Reviewer: Messoud Efendiev (Berlin) MSC: 37L30 35Q35 37K40 PDF BibTeX XML Cite \textit{Y. You}, Nonlinear Anal., Theory Methods Appl. 30, No. 7, 4643--4654 (1997; Zbl 0927.37058) Full Text: DOI
Elie, F.; Chikhaoui, A.; Randriamampianina, A.; Bontoux, P.; Roux, B. Spectral approximation for Boussinesq double diffusion. (English) Zbl 0552.76072 Numerical methods in fluid mechanics, Proc. 5th GAMM-Conf., Rome 1983, Notes Numer. Fluid Mech. 7, 57-64 (1984). MSC: 76R99 76M99 PDF BibTeX XML