Cao, Daomin; Wang, Guodong; Zuo, Bijun Existence of steady symmetric vortex patch in a disk. (English) Zbl 07312803 J. Math. Fluid Mech. 23, No. 1, Paper No. 20, 13 p. (2021). MSC: 76B47 76M30 76B03 35Q31 PDF BibTeX XML Cite \textit{D. Cao} et al., J. Math. Fluid Mech. 23, No. 1, Paper No. 20, 13 p. (2021; Zbl 07312803) Full Text: DOI
Cao, Daomin; Wan, Jie; Zhan, Weicheng Desingularization of vortex rings in 3 dimensional Euler flows. (English) Zbl 1451.35120 J. Differ. Equations 270, 1258-1297 (2021). MSC: 35Q31 76B47 35B40 PDF BibTeX XML Cite \textit{D. Cao} et al., J. Differ. Equations 270, 1258--1297 (2021; Zbl 1451.35120) Full Text: DOI
Cao, Daomin; Wang, Guodong; Zhan, Weicheng Desingularization of vortices for two-dimensional steady Euler flows via the vorticity method. (English) Zbl 07269950 SIAM J. Math. Anal. 52, No. 6, 5363-5388 (2020). MSC: 76B47 76B03 35Q31 PDF BibTeX XML Cite \textit{D. Cao} et al., SIAM J. Math. Anal. 52, No. 6, 5363--5388 (2020; Zbl 07269950) Full Text: DOI
Dekeyser, Justin; Van Schaftingen, Jean Vortex motion for the lake equations. (English) Zbl 1443.76117 Commun. Math. Phys. 375, No. 2, 1459-1501 (2020). MSC: 76B47 76U60 76M45 86A05 PDF BibTeX XML Cite \textit{J. Dekeyser} and \textit{J. Van Schaftingen}, Commun. Math. Phys. 375, No. 2, 1459--1501 (2020; Zbl 1443.76117) Full Text: DOI
Cao, Daomin; Wan, Jie; Wang, Guodong Steady vortex patch with polygonal symmetry for the planar Euler equations in a disc. (English) Zbl 1433.35250 Nonlinear Anal., Real World Appl. 51, Article ID 103008, 19 p. (2020). MSC: 35Q31 76B47 76E30 35J20 35Q35 35J60 35A15 PDF BibTeX XML Cite \textit{D. Cao} et al., Nonlinear Anal., Real World Appl. 51, Article ID 103008, 19 p. (2020; Zbl 1433.35250) Full Text: DOI
Cao, Daomin; Guo, Yuxia; Peng, Shuangjie; Yan, Shusen Local uniqueness for vortex patch problem in incompressible planar steady flow. (English. French summary) Zbl 1436.35153 J. Math. Pures Appl. (9) 131, 251-289 (2019). Reviewer: Alain Brillard (Riedisheim) MSC: 35J60 35J25 35Q05 PDF BibTeX XML Cite \textit{D. Cao} et al., J. Math. Pures Appl. (9) 131, 251--289 (2019; Zbl 1436.35153) Full Text: DOI
Cao, Daomin; Wang, Guodong Steady vortex patches with opposite rotation directions in a planar ideal fluid. (English) Zbl 1450.76003 Calc. Var. Partial Differ. Equ. 58, No. 2, Paper No. 75, 17 p. (2019). Reviewer: Hakan Adıgüzel (Serdivan) MSC: 76B03 76B47 76M30 35Q31 49J40 PDF BibTeX XML Cite \textit{D. Cao} and \textit{G. Wang}, Calc. Var. Partial Differ. Equ. 58, No. 2, Paper No. 75, 17 p. (2019; Zbl 1450.76003) Full Text: DOI
Cao, Daomin; Peng, Shuangjie; Yan, Shusen Regularization of planar vortices for the incompressible flow. (English) Zbl 1438.35191 Acta Math. Sci., Ser. B, Engl. Ed. 38, No. 5, 1443-1467 (2018). MSC: 35J91 35J20 35Q35 76B47 PDF BibTeX XML Cite \textit{D. Cao} et al., Acta Math. Sci., Ser. B, Engl. Ed. 38, No. 5, 1443--1467 (2018; Zbl 1438.35191) Full Text: DOI
Li, Yi; Peng, Shuangjie Multi-peak solutions to two types of free boundary problems. (English) Zbl 1333.35023 Calc. Var. Partial Differ. Equ. 54, No. 1, 163-182 (2015). Reviewer: Satoshi Tanaka (Okayama) MSC: 35J20 35J61 PDF BibTeX XML Cite \textit{Y. Li} and \textit{S. Peng}, Calc. Var. Partial Differ. Equ. 54, No. 1, 163--182 (2015; Zbl 1333.35023) Full Text: DOI
Cao, Daomin; Peng, Shuangjie; Yan, Shusen Planar vortex patch problem in incompressible steady flow. (English) Zbl 06380404 Adv. Math. 270, 263-301 (2015). MSC: 35Q31 37 PDF BibTeX XML Cite \textit{D. Cao} et al., Adv. Math. 270, 263--301 (2015; Zbl 06380404) Full Text: DOI
Cao, Daomin; Liu, Zhongyuan; Wei, Juncheng Regularization of point vortices pairs for the Euler equation in dimension two. (English) Zbl 1293.35223 Arch. Ration. Mech. Anal. 212, No. 1, 179-217 (2014). MSC: 35Q31 76B47 35B65 PDF BibTeX XML Cite \textit{D. Cao} et al., Arch. Ration. Mech. Anal. 212, No. 1, 179--217 (2014; Zbl 1293.35223) Full Text: DOI arXiv
de Valeriola, Sébastien; Van Schaftingen, Jean Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem. (English) Zbl 1294.35083 Arch. Ration. Mech. Anal. 210, No. 2, 409-450 (2013). MSC: 35Q31 76B47 76B03 76B15 35J61 PDF BibTeX XML Cite \textit{S. de Valeriola} and \textit{J. Van Schaftingen}, Arch. Ration. Mech. Anal. 210, No. 2, 409--450 (2013; Zbl 1294.35083) Full Text: DOI arXiv
Wang, Yuan-Ming; Wu, Wen-Jia; Scalia, Massimo Numerov’s method for a class of nonlinear multipoint boundary value problems. (English) Zbl 1264.65115 Math. Probl. Eng. 2012, Article ID 316852, 29 p. (2012). MSC: 65L10 65L12 34B10 PDF BibTeX XML Cite \textit{Y.-M. Wang} et al., Math. Probl. Eng. 2012, Article ID 316852, 29 p. (2012; Zbl 1264.65115) Full Text: DOI
Pandey, R. K.; Barnwal, A. K. Multiple solutions for nonlinear doubly singular three-point boundary value problems with derivative dependence. (English) Zbl 1250.34018 Int. J. Differ. Equ. 2012, Article ID 838947, 21 p. (2012). MSC: 34B18 34B10 34B16 47N20 PDF BibTeX XML Cite \textit{R. K. Pandey} and \textit{A. K. Barnwal}, Int. J. Differ. Equ. 2012, Article ID 838947, 21 p. (2012; Zbl 1250.34018) Full Text: DOI
Li, Yi; Peng, Shuangjie Multiple solutions for an elliptic problem related to vortex pairs. (English) Zbl 1214.31005 J. Differ. Equations 250, No. 8, 3448-3472 (2011). MSC: 31A25 PDF BibTeX XML Cite \textit{Y. Li} and \textit{S. Peng}, J. Differ. Equations 250, No. 8, 3448--3472 (2011; Zbl 1214.31005) Full Text: DOI
Smets, Didier; Van Schaftingen, Jean Desingularization of vortices for the Euler equation. (English) Zbl 1228.35171 Arch. Ration. Mech. Anal. 198, No. 3, 869-925 (2010). Reviewer: Bernard Ducomet (Bruyères le Châtel) MSC: 35Q31 76B47 PDF BibTeX XML Cite \textit{D. Smets} and \textit{J. Van Schaftingen}, Arch. Ration. Mech. Anal. 198, No. 3, 869--925 (2010; Zbl 1228.35171) Full Text: DOI arXiv
Wang, Yuan-Ming On 2nth-order nonlinear multi-point boundary value problems. (English) Zbl 1206.34036 Math. Comput. Modelling 51, No. 9-10, 1251-1259 (2010). MSC: 34B10 34A45 PDF BibTeX XML Cite \textit{Y.-M. Wang}, Math. Comput. Modelling 51, No. 9--10, 1251--1259 (2010; Zbl 1206.34036) Full Text: DOI
Bensid, Sabri; Bouguima, S. M. On a free boundary problem. (English) Zbl 1138.35418 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 8, 2328-2348 (2008). MSC: 35R35 35J65 PDF BibTeX XML Cite \textit{S. Bensid} and \textit{S. M. Bouguima}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 8, 2328--2348 (2008; Zbl 1138.35418) Full Text: DOI
Zou, Yongkui; Hu, Qingwan; Zhang, Ran On numerical studies of multi-point boundary value problem and its fold bifurcation. (English) Zbl 1112.65069 Appl. Math. Comput. 185, No. 1, 527-537 (2007). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 65L10 34B10 34B15 34C23 PDF BibTeX XML Cite \textit{Y. Zou} et al., Appl. Math. Comput. 185, No. 1, 527--537 (2007; Zbl 1112.65069) Full Text: DOI
Ma, Ruyun; Thompson, Bevan Global behavior of positive solutions of nonlinear three-point boundary value problems. (English) Zbl 1069.34016 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 60, No. 4, 685-701 (2005). Reviewer: Narahari Parhi (Bhubaneswar) MSC: 34B10 34B18 PDF BibTeX XML Cite \textit{R. Ma} and \textit{B. Thompson}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 60, No. 4, 685--701 (2005; Zbl 1069.34016) Full Text: DOI
Elcrat, Alan R.; Miller, Kenneth G. A monotone iteration for concentrated vortices. (English) Zbl 1160.35490 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 6, 777-789 (2001). Reviewer: Erich Miersemann (Leipzig)(MR1825781) MSC: 35P30 35A35 76B47 PDF BibTeX XML Cite \textit{A. R. Elcrat} and \textit{K. G. Miller}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 6, 777--789 (2001; Zbl 1160.35490) Full Text: DOI Link
Marchioro, Carlo Large smoke rings with concentrated vorticity. (English) Zbl 0969.76014 J. Math. Phys. 40, No. 2, 869-883 (1999). MSC: 76B47 35Q35 PDF BibTeX XML Cite \textit{C. Marchioro}, J. Math. Phys. 40, No. 2, 869--883 (1999; Zbl 0969.76014) Full Text: DOI
Ma, Ruyun Existence theorems for a second order three-point boundary value problem. (English) Zbl 0879.34025 J. Math. Anal. Appl. 212, No. 2, 430-442 (1997). MSC: 34B10 PDF BibTeX XML Cite \textit{R. Ma}, J. Math. Anal. Appl. 212, No. 2, 430--442 (1997; Zbl 0879.34025) Full Text: DOI
Boucherif, Abdelkader; Bouguima, Sidi Mohammed On a free boundary problem. (English) Zbl 0860.35148 Math. Methods Appl. Sci. 19, No. 15, 1257-1264 (1996). MSC: 35R35 35R05 35J25 PDF BibTeX XML Cite \textit{A. Boucherif} and \textit{S. M. Bouguima}, Math. Methods Appl. Sci. 19, No. 15, 1257--1264 (1996; Zbl 0860.35148) Full Text: DOI
Yang, Jianfu Global vortex rings and asymptotic behaviour. (English) Zbl 0845.76017 Nonlinear Anal., Theory Methods Appl. 25, No. 5, 531-546 (1995). Reviewer: A.Berezovski (Tallinn) MSC: 76B47 35Q35 PDF BibTeX XML Cite \textit{J. Yang}, Nonlinear Anal., Theory Methods Appl. 25, No. 5, 531--546 (1995; Zbl 0845.76017) Full Text: DOI
Tadie On the bifurcation of steady vortex rings from a Green function. (English) Zbl 0853.35135 Math. Proc. Camb. Philos. Soc. 116, No. 3, 555-568 (1994). Reviewer: V.A.Sava (Iaşi) MSC: 35R35 76B47 PDF BibTeX XML Cite \textit{Tadie}, Math. Proc. Camb. Philos. Soc. 116, No. 3, 555--568 (1994; Zbl 0853.35135) Full Text: DOI
Ambrosetti, Antonio Critical points and nonlinear variational problems. (English) Zbl 0766.49006 Mém. Soc. Math. Fr., Nouv. Sér. 49, 139 p. (1992). Reviewer: J.F.Bonnans (Le Chesnay) MSC: 49J20 49J15 PDF BibTeX XML Cite \textit{A. Ambrosetti}, Mém. Soc. Math. Fr., Nouv. Sér. 49, 139 p. (1992; Zbl 0766.49006) Full Text: DOI Numdam EuDML
Stuart, Andrew Singular limits in free boundary problems. (English) Zbl 0732.35108 Rocky Mt. J. Math. 21, No. 2, 809-811 (1991). MSC: 35R35 35P20 35B32 35R05 PDF BibTeX XML Cite \textit{A. Stuart}, Rocky Mt. J. Math. 21, No. 2, 809--811 (1991; Zbl 0732.35108) Full Text: DOI
Stuart, Andrew Corrections to: “Singular limits in free boundary problems”. (English) Zbl 0793.35135 Rocky Mt. J. Math. 21, No. 3, 1172 (1991). MSC: 35R35 35P20 35B32 35R05 PDF BibTeX XML Cite \textit{A. Stuart}, Rocky Mt. J. Math. 21, No. 3, 1172 (1991; Zbl 0793.35135) Full Text: DOI
Chen, Y. Y. The nonlinear desingularization phenomenon in the Abelian Higgs model for isotropic solutions. (English) Zbl 0694.35205 J. Math. Phys. 29, No. 8, 1896-1900 (1988). MSC: 35Q99 35B40 81T08 PDF BibTeX XML Cite \textit{Y. Y. Chen}, J. Math. Phys. 29, No. 8, 1896--1900 (1988; Zbl 0694.35205) Full Text: DOI
Keady, G.; Kloeden, P. E. An elliptic boundary-value problem with a discontinuous nonlinearity. II. (English) Zbl 0647.35029 Proc. R. Soc. Edinb., Sect. A 105, 23-36 (1987). MSC: 35J65 35R05 35B40 PDF BibTeX XML Cite \textit{G. Keady} and \textit{P. E. Kloeden}, Proc. R. Soc. Edinb., Sect. A, Math. 105, 23--36 (1987; Zbl 0647.35029) Full Text: DOI
Boucherif, Abdelkader Nonlinear multipoint boundary value problems. (English) Zbl 0607.34014 Nonlinear Anal., Theory Methods Appl. 10, 957-964 (1986). MSC: 34B10 34B15 34A34 PDF BibTeX XML Cite \textit{A. Boucherif}, Nonlinear Anal., Theory Methods Appl. 10, 957--964 (1986; Zbl 0607.34014) Full Text: DOI
Elliott, Charles M.; Friedman, Avner The contact set of a rigid body partially supported by a membrane. (English) Zbl 0588.73196 Nonlinear Anal., Theory Methods Appl. 10, 251-276 (1986). Reviewer: H.Bufler MSC: 74A55 74M15 49J40 74G30 74H25 PDF BibTeX XML Cite \textit{C. M. Elliott} and \textit{A. Friedman}, Nonlinear Anal., Theory Methods Appl. 10, 251--276 (1986; Zbl 0588.73196) Full Text: DOI
Berestycki, Henri; Fernández-Cara, Enrique; Glowinski, Roland A numerical study of some questions in vortex rings theory. (English) Zbl 0594.76021 RAIRO, Anal. Numér. 18, 7-85 (1984). MSC: 76B47 76M99 65M50 65N50 PDF BibTeX XML Cite \textit{H. Berestycki} et al., RAIRO, Anal. Numér. 18, 7--85 (1984; Zbl 0594.76021) Full Text: DOI EuDML
Turkington, Bruce On steady vortex flow in two dimensions. I. (English) Zbl 0523.76014 Commun. Partial Differ. Equations 8, 999-1030 (1983). MSC: 76B47 49S05 35B40 35A05 PDF BibTeX XML Cite \textit{B. Turkington}, Commun. Partial Differ. Equations 8, 999--1030 (1983; Zbl 0523.76014) Full Text: DOI
Keady, G. An elliptic boundary-value problem with a discontinuous nonlinearity. (English) Zbl 0511.35032 Proc. R. Soc. Edinb., Sect. A 91, 161-174 (1981). MSC: 35J65 35J25 35B99 76B47 49J40 PDF BibTeX XML Cite \textit{G. Keady}, Proc. R. Soc. Edinb., Sect. A, Math. 91, 161--174 (1981; Zbl 0511.35032) Full Text: DOI
Friedman, Avner; Turkington, Bruce Vortex rings: existence and asymptotic estimates. (English) Zbl 0497.76031 Trans. Am. Math. Soc. 268, 1-37 (1981). MSC: 76B47 76G25 49S05 31A15 35J05 35J20 PDF BibTeX XML Cite \textit{A. Friedman} and \textit{B. Turkington}, Trans. Am. Math. Soc. 268, 1--37 (1981; Zbl 0497.76031) Full Text: DOI
Fraenkel, L. E. A lower bound for electrostatic capacity in the plane. (English) Zbl 0466.31007 Proc. R. Soc. Edinb., Sect. A 88, 267-273 (1981). MSC: 31A15 78A30 PDF BibTeX XML Cite \textit{L. E. Fraenkel}, Proc. R. Soc. Edinb., Sect. A, Math. 88, 267--273 (1981; Zbl 0466.31007) Full Text: DOI