Cao, Daomin; Wan, Jie Structure of Green’s function of elliptic equations and helical vortex patches for 3D incompressible Euler equations. (English) Zbl 07808067 Math. Ann. 388, No. 3, 2627-2669 (2024). MSC: 35Q31 76B47 76U05 35J15 35J08 35C07 35B50 35B40 35B35 35A15 35A21 PDFBibTeX XMLCite \textit{D. Cao} and \textit{J. Wan}, Math. Ann. 388, No. 3, 2627--2669 (2024; Zbl 07808067) Full Text: DOI arXiv
Cao, Daomin; Wan, Jie Desingularization of 3D steady Euler equations with helical symmetry. (English) Zbl 1527.35232 Calc. Var. Partial Differ. Equ. 62, No. 9, Paper No. 259, 29 p. (2023). MSC: 35Q31 76B47 35B40 35J61 35B06 35A15 PDFBibTeX XMLCite \textit{D. Cao} and \textit{J. Wan}, Calc. Var. Partial Differ. Equ. 62, No. 9, Paper No. 259, 29 p. (2023; Zbl 1527.35232) Full Text: DOI arXiv
Cao, Daomin; Lai, Shanfa; Qin, Guolin A note on the existence of stationary vortex patches for the SQG equation in bounded domain. (English) Zbl 1527.76007 Proc. Am. Math. Soc. 151, No. 11, 4881-4891 (2023). Reviewer: Anatoliy K. Prykarpatsky (Kraków) MSC: 76B47 35Q31 PDFBibTeX XMLCite \textit{D. Cao} et al., Proc. Am. Math. Soc. 151, No. 11, 4881--4891 (2023; Zbl 1527.76007) Full Text: DOI
Cao, Daomin; Qin, Guolin; Zhan, Weicheng; Zou, Changjun Kármán vortex street for the generalized surface quasi-geostrophic equation. (English) Zbl 1516.76018 Calc. Var. Partial Differ. Equ. 62, No. 6, Paper No. 168, 35 p. (2023). MSC: 76B47 76B03 76M30 35Q31 PDFBibTeX XMLCite \textit{D. Cao} et al., Calc. Var. Partial Differ. Equ. 62, No. 6, Paper No. 168, 35 p. (2023; Zbl 1516.76018) Full Text: DOI arXiv
Cao, Daomin; Qin, Guolin; Zou, Changjun Existence of stationary vortex sheets for the 2D incompressible Euler equation. (English) Zbl 1514.76017 Can. J. Math. 75, No. 3, 828-853 (2023). MSC: 76B47 76B03 35Q31 PDFBibTeX XMLCite \textit{D. Cao} et al., Can. J. Math. 75, No. 3, 828--853 (2023; Zbl 1514.76017) Full Text: DOI
Cao, Daomin; Lai, Shanfa Helical symmetry vortices for 3D incompressible Euler equations. (English) Zbl 07677449 J. Differ. Equations 360, 67-89 (2023). MSC: 76B47 35Q35 PDFBibTeX XMLCite \textit{D. Cao} and \textit{S. Lai}, J. Differ. Equations 360, 67--89 (2023; Zbl 07677449) Full Text: DOI
Cao, Daomin; Qin, Guolin; Zhan, Weicheng; Zou, Changjun Global solutions for the generalized SQG equation and rearrangements. (English) Zbl 1523.76113 Trans. Am. Math. Soc. 376, No. 3, 2181-2211 (2023). MSC: 76U60 76B47 35Q35 PDFBibTeX XMLCite \textit{D. Cao} et al., Trans. Am. Math. Soc. 376, No. 3, 2181--2211 (2023; Zbl 1523.76113) Full Text: DOI arXiv
Cao, Daomin; Wan, Jie Helical vortices with small cross-section for 3D incompressible Euler equation. (English) Zbl 1508.76027 J. Funct. Anal. 284, No. 7, Article ID 109836, 48 p. (2023). MSC: 76B47 76B03 35Q31 PDFBibTeX XMLCite \textit{D. Cao} and \textit{J. Wan}, J. Funct. Anal. 284, No. 7, Article ID 109836, 48 p. (2023; Zbl 1508.76027) Full Text: DOI arXiv
Cao, Daomin; Yu, Weilin; Zou, Changjun Local uniqueness of vortices for 2D steady Euler flow in a bounded domain. (English) Zbl 1496.76036 J. Funct. Anal. 283, No. 8, Article ID 109603, 43 p. (2022). MSC: 76B47 76B03 76E30 35Q31 PDFBibTeX XMLCite \textit{D. Cao} et al., J. Funct. Anal. 283, No. 8, Article ID 109603, 43 p. (2022; Zbl 1496.76036) Full Text: DOI arXiv
Cao, Daomin; Qin, Guolin; Zhan, Weicheng; Zou, Changjun On the global classical solutions for the generalized SQG equation. (English) Zbl 1506.35242 J. Funct. Anal. 283, No. 2, Article ID 109503, 37 p. (2022). MSC: 35Q86 35Q31 86A05 76B03 35A15 35A09 35B65 35D30 35C07 35A01 35A02 PDFBibTeX XMLCite \textit{D. Cao} et al., J. Funct. Anal. 283, No. 2, Article ID 109503, 37 p. (2022; Zbl 1506.35242) Full Text: DOI arXiv
Cao, Daomin; Wan, Jie Multiscale steady vortex patches for 2D incompressible Euler equations. (English) Zbl 1513.76052 SIAM J. Math. Anal. 54, No. 2, 1488-1514 (2022). MSC: 76B47 35Q31 76M30 PDFBibTeX XMLCite \textit{D. Cao} and \textit{J. Wan}, SIAM J. Math. Anal. 54, No. 2, 1488--1514 (2022; Zbl 1513.76052) Full Text: DOI
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 PDFBibTeX XMLCite \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
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 PDFBibTeX XMLCite \textit{D. Cao} et al., J. Differ. Equations 299, 429--462 (2021; Zbl 1476.35280) Full Text: DOI arXiv
Cao, Daomin; Dai, Wei; Qin, Guolin Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians. (English) Zbl 1465.35388 Trans. Am. Math. Soc. 374, No. 7, 4781-4813 (2021). MSC: 35R11 35C15 35B53 35B06 35J92 PDFBibTeX XMLCite \textit{D. Cao} et al., Trans. Am. Math. Soc. 374, No. 7, 4781--4813 (2021; Zbl 1465.35388) Full Text: DOI arXiv
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 PDFBibTeX XMLCite \textit{D. Cao} et al., J. Differ. Equations 270, 1258--1297 (2021; Zbl 1451.35120) Full Text: DOI arXiv
Cao, Daomin; Liu, Zhongyuan; Peng, Shuangjie Sign-changing bubble tower solutions for the supercritical Hénon-type equations. (English) Zbl 1403.35108 Ann. Mat. Pura Appl. (4) 197, No. 4, 1227-1246 (2018). MSC: 35J61 35J05 35J25 PDFBibTeX XMLCite \textit{D. Cao} et al., Ann. Mat. Pura Appl. (4) 197, No. 4, 1227--1246 (2018; Zbl 1403.35108) Full Text: DOI
Cao, Daomin; Li, Shuanglong; Liu, Zhongyuan Nodal solutions for a supercritical semilinear problem with variable exponent. (English) Zbl 1392.35156 Calc. Var. Partial Differ. Equ. 57, No. 2, Paper No. 38, 19 p. (2018). MSC: 35J91 35J25 35J20 PDFBibTeX XMLCite \textit{D. Cao} et al., Calc. Var. Partial Differ. Equ. 57, No. 2, Paper No. 38, 19 p. (2018; Zbl 1392.35156) Full Text: DOI
Cao, Daomin; Li, Shuanglong; Luo, Peng Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations. (English) Zbl 1338.35404 Calc. Var. Partial Differ. Equ. 54, No. 4, 4037-4063 (2015). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q55 35J20 35J60 35B09 PDFBibTeX XMLCite \textit{D. Cao} et al., Calc. Var. Partial Differ. Equ. 54, No. 4, 4037--4063 (2015; Zbl 1338.35404) Full Text: DOI arXiv
Cao, Daomin; Peng, Shuangjie Semi-classical bound states for Schrödinger equations with potentials vanishing or unbounded at infinity. (English) Zbl 1185.35248 Commun. Partial Differ. Equations 34, No. 12, 1566-1591 (2009). Reviewer: M. Marin (Brasov) MSC: 35Q55 35J20 35J60 81Q05 PDFBibTeX XMLCite \textit{D. Cao} and \textit{S. Peng}, Commun. Partial Differ. Equations 34, No. 12, 1566--1591 (2009; Zbl 1185.35248) Full Text: DOI
Cao, Daomin; Noussair, Ezzat S.; Yan, Shusen Multiscale-bump standing waves with a critical frequency for nonlinear Schrödinger equations. (English) Zbl 1167.35042 Trans. Am. Math. Soc. 360, No. 7, 3813-3837 (2008). MSC: 35Q55 35B35 35B38 35J20 PDFBibTeX XMLCite \textit{D. Cao} et al., Trans. Am. Math. Soc. 360, No. 7, 3813--3837 (2008; Zbl 1167.35042) Full Text: DOI
Cao, Daomin; Peng, Shuangjie Multi-bump bound states of Schrödinger equations with a critical frequency. (English) Zbl 1123.35061 Math. Ann. 336, No. 4, 925-948 (2006). MSC: 35Q55 35J60 35B33 35A15 47J30 58E05 PDFBibTeX XMLCite \textit{D. Cao} and \textit{S. Peng}, Math. Ann. 336, No. 4, 925--948 (2006; Zbl 1123.35061) Full Text: DOI
Cao, Daomin; Tang, Zhongwei Existence and uniqueness of multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields. (English) Zbl 1357.35258 J. Differ. Equations 222, No. 2, 381-424 (2006). MSC: 35Q55 81V10 35J60 35B33 PDFBibTeX XMLCite \textit{D. Cao} and \textit{Z. Tang}, J. Differ. Equations 222, No. 2, 381--424 (2006; Zbl 1357.35258) Full Text: DOI
Cao, Daomin; Noussair, Ezzat S. Multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations. (English) Zbl 1063.35142 J. Differ. Equations 203, No. 2, 292-312 (2004). Reviewer: Andrew Pickering (Madrid) MSC: 35Q55 37K40 81Q05 PDFBibTeX XMLCite \textit{D. Cao} and \textit{E. S. Noussair}, J. Differ. Equations 203, No. 2, 292--312 (2004; Zbl 1063.35142) Full Text: DOI
Cao, Daomin; Noussair, Ezzat S. Multi-peak solutions for a singularly perturbed semilinear elliptic problem. (English) Zbl 0966.35039 J. Differ. Equations 166, No. 2, 266-289 (2000). Reviewer: Mihai Pascu (Bucureşti) MSC: 35J60 35B25 35J65 35J20 35B05 35A05 PDFBibTeX XMLCite \textit{D. Cao} and \textit{E. S. Noussair}, J. Differ. Equations 166, No. 2, 266--289 (2000; Zbl 0966.35039) Full Text: DOI