Cao, Daomin; Wan, Jie Multiscale steady vortex patches for 2D incompressible Euler equations. (English) Zbl 07493739 SIAM J. Math. Anal. 54, No. 2, 1488-1514 (2022). MSC: 76B47 35Q31 PDF BibTeX XML Cite \textit{D. Cao} and \textit{J. Wan}, SIAM J. Math. Anal. 54, No. 2, 1488--1514 (2022; Zbl 07493739) Full Text: DOI OpenURL
Cao, Daomin; Lai, Shanfa; Zhan, Weicheng Traveling vortex pairs for 2D incompressible Euler equations. (English) Zbl 1473.35221 Calc. Var. Partial Differ. Equ. 60, No. 5, Paper No. 190, 16 p. (2021). MSC: 35J60 35Q31 76B47 PDF BibTeX XML Cite \textit{D. Cao} et al., Calc. Var. Partial Differ. Equ. 60, No. 5, Paper No. 190, 16 p. (2021; Zbl 1473.35221) Full Text: DOI arXiv OpenURL
Cao, Daomin; Qin, Guolin; Zhan, Weicheng; Zou, Changjun Existence and regularity of co-rotating and traveling-wave vortex solutions for the generalized SQG equation. (English) Zbl 1476.35280 J. Differ. Equations 299, 429-462 (2021). MSC: 35Q86 35Q31 86A05 76U60 76B47 35C07 35A01 35A02 PDF BibTeX XML Cite \textit{D. Cao} et al., J. Differ. Equations 299, 429--462 (2021; Zbl 1476.35280) Full Text: DOI arXiv OpenURL
Cao, Daomin; Wang, Guodong Nonlinear stability of planar vortex patches in an ideal fluid. (English) Zbl 1467.76032 J. Math. Fluid Mech. 23, No. 3, Paper No. 58, 16 p. (2021). MSC: 76E30 76B47 76M30 35Q31 PDF BibTeX XML Cite \textit{D. Cao} and \textit{G. Wang}, J. Math. Fluid Mech. 23, No. 3, Paper No. 58, 16 p. (2021; Zbl 1467.76032) Full Text: DOI arXiv OpenURL
Cao, Daomin; Wang, Guodong; Zhan, Weicheng Steady vortex patches near a nontrivial irrotational flow. (English) Zbl 1470.76025 Sci. China, Math. 64, No. 5, 947-962 (2021). MSC: 76B47 76B03 76M30 35Q31 PDF BibTeX XML Cite \textit{D. Cao} et al., Sci. China, Math. 64, No. 5, 947--962 (2021; Zbl 1470.76025) Full Text: DOI arXiv OpenURL
Cao, Daomin; Wang, Guodong; Zuo, Bijun Existence of steady symmetric vortex patch in a disk. (English) Zbl 1458.76019 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 1458.76019) Full Text: DOI arXiv OpenURL
Cao, Daomin; Wan, Jie; Wang, Guodong; Zhan, Weicheng Rotating vortex patches for the planar Euler equations in a disk. (English) Zbl 1455.35180 J. Differ. Equations 275, 509-532 (2021). MSC: 35Q31 35A15 35B35 76B47 PDF BibTeX XML Cite \textit{D. Cao} et al., J. Differ. Equations 275, 509--532 (2021; Zbl 1455.35180) Full Text: DOI arXiv OpenURL
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 arXiv OpenURL
Cao, Daomin; Wang, Guodong Existence of steady multiple vortex patches to the vortex-wave system. (English) Zbl 1458.35159 Pac. J. Math. 308, No. 2, 257-279 (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 35J50 35Q35 PDF BibTeX XML Cite \textit{D. Cao} and \textit{G. Wang}, Pac. J. Math. 308, No. 2, 257--279 (2020; Zbl 1458.35159) Full Text: DOI arXiv OpenURL
Cao, Daomin; Wang, Guodong; Zhan, Weicheng Desingularization of vortices for two-dimensional steady Euler flows via the vorticity method. (English) Zbl 1461.76082 SIAM J. Math. Anal. 52, No. 6, 5363-5388 (2020). MSC: 76B47 76B03 76E30 76M23 35Q31 PDF BibTeX XML Cite \textit{D. Cao} et al., SIAM J. Math. Anal. 52, No. 6, 5363--5388 (2020; Zbl 1461.76082) Full Text: DOI arXiv OpenURL
Cao, Daomin; Wang, Guodong A note on steady vortex flows in two dimensions. (English) Zbl 1431.33015 Proc. Am. Math. Soc. 148, No. 3, 1153-1159 (2020). MSC: 33C55 33C50 42B15 42C10 PDF BibTeX XML Cite \textit{D. Cao} and \textit{G. Wang}, Proc. Am. Math. Soc. 148, No. 3, 1153--1159 (2020; Zbl 1431.33015) Full Text: DOI OpenURL
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 OpenURL
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 arXiv OpenURL
Cao, Daomin; Wang, Guodong Steady vortex patch solutions to the vortex-wave system. (English) Zbl 1411.76027 Nonlinearity 32, No. 5, 1882-1904 (2019). MSC: 76D17 35J20 35Q31 PDF BibTeX XML Cite \textit{D. Cao} and \textit{G. Wang}, Nonlinearity 32, No. 5, 1882--1904 (2019; Zbl 1411.76027) Full Text: DOI arXiv OpenURL
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 arXiv OpenURL
Cao, Daomin; Wan, Jie; Wang, Guodong Nonlinear orbital stability for planar vortex patches. (English) Zbl 1444.76036 Proc. Am. Math. Soc. 147, No. 2, 775-784 (2019). Reviewer: Kai Schneider (Marseille) MSC: 76B47 35Q31 35B35 PDF BibTeX XML Cite \textit{D. Cao} et al., Proc. Am. Math. Soc. 147, No. 2, 775--784 (2019; Zbl 1444.76036) Full Text: DOI arXiv OpenURL
Cao, Daomin; Liu, Zhongyuan Steady vortex solutions to two dimensional incompressible Euler equation. (Chinese. English summary) Zbl 07494592 Sci. Sin., Math. 48, No. 1, 3-14 (2018). MSC: 35Q31 35B40 PDF BibTeX XML Cite \textit{D. Cao} and \textit{Z. Liu}, Sci. Sin., Math. 48, No. 1, 3--14 (2018; Zbl 07494592) Full Text: DOI OpenURL
Cao, Daomin; Peng, Shuangjie; Yan, Shusen Planar vortex patch problem in incompressible steady flow. (English) Zbl 1480.35318 Adv. Math. 270, 263-301 (2015). MSC: 35Q31 35J61 35A15 35A01 76B47 35R35 PDF BibTeX XML Cite \textit{D. Cao} et al., Adv. Math. 270, 263--301 (2015; Zbl 1480.35318) Full Text: DOI OpenURL
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 OpenURL