Jeong, In-Jee; Kim, Junha Strong ill-posedness for SQG in critical Sobolev spaces. (English) Zbl 07807512 Anal. PDE 17, No. 1, 133-170 (2024). MSC: 35Q35 76B47 76U60 35R25 86A05 35D30 35A01 PDFBibTeX XMLCite \textit{I.-J. Jeong} and \textit{J. Kim}, Anal. PDE 17, No. 1, 133--170 (2024; Zbl 07807512) Full Text: DOI arXiv
Cobb, Dimitri Bounded solutions in incompressible hydrodynamics. (English) Zbl 07787698 J. Funct. Anal. 286, No. 5, Article ID 110290, 49 p. (2024). MSC: 35Q31 35Q35 35A02 76W05 35B30 35S30 PDFBibTeX XMLCite \textit{D. Cobb}, J. Funct. Anal. 286, No. 5, Article ID 110290, 49 p. (2024; Zbl 07787698) Full Text: DOI arXiv
Drivas, Theodore D.; Elgindi, Tarek M. Singularity formation in the incompressible Euler equation in finite and infinite time. (English) Zbl 07803735 EMS Surv. Math. Sci. 10, No. 1, 1-100 (2023). MSC: 35Q31 76B03 35B40 35C06 35B07 35A01 35A02 PDFBibTeX XMLCite \textit{T. D. Drivas} and \textit{T. M. Elgindi}, EMS Surv. Math. Sci. 10, No. 1, 1--100 (2023; Zbl 07803735) Full Text: DOI arXiv
Zhao, Jiefeng Mild ill-posedness for 2D magneto-micropolar fluid equations near a background magnetic field. (English) Zbl 1527.35312 SIAM J. Math. Anal. 55, No. 5, 5967-5992 (2023). MSC: 35Q35 35Q86 35R25 76B03 76W05 76A05 PDFBibTeX XMLCite \textit{J. Zhao}, SIAM J. Math. Anal. 55, No. 5, 5967--5992 (2023; Zbl 1527.35312) Full Text: DOI
Fang, Hui; Bie, Qunyi Mild ill-posedness in \(L^\infty\) for 2D magnetohydrodynamic system with damping. (English) Zbl 1527.35275 J. Differ. Equations 377, 519-543 (2023). MSC: 35Q35 35B35 47J06 35R25 PDFBibTeX XMLCite \textit{H. Fang} and \textit{Q. Bie}, J. Differ. Equations 377, 519--543 (2023; Zbl 1527.35275) Full Text: DOI
Constantin, Peter; Pasqualotto, Federico Magnetic relaxation of a Voigt-MHD system. (English) Zbl 07727605 Commun. Math. Phys. 402, No. 2, 1931-1952 (2023). MSC: 35Q35 76W05 76B03 35B65 PDFBibTeX XMLCite \textit{P. Constantin} and \textit{F. Pasqualotto}, Commun. Math. Phys. 402, No. 2, 1931--1952 (2023; Zbl 07727605) Full Text: DOI arXiv
Wu, Wenpei; Wang, Yong On the half-space or exterior problems of the 3D compressible elastic Navier-Stokes-Poisson equations. (English) Zbl 07723845 SIAM J. Math. Anal. 55, No. 4, 2996-3043 (2023). MSC: 76A10 76W05 76N10 35Q35 PDFBibTeX XMLCite \textit{W. Wu} and \textit{Y. Wang}, SIAM J. Math. Anal. 55, No. 4, 2996--3043 (2023; Zbl 07723845) Full Text: DOI arXiv
Kiselev, Alexander; Luo, Xiaoyutao Illposedness of \(C^2\) vortex patches. (English) Zbl 1516.35316 Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 57, 49 p. (2023). MSC: 35Q31 76B47 76B03 35A01 35A02 35B65 35D30 PDFBibTeX XMLCite \textit{A. Kiselev} and \textit{X. Luo}, Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 57, 49 p. (2023; Zbl 1516.35316) Full Text: DOI arXiv
Choi, Kyudong; Jeong, In-Jee Filamentation near Hill’s vortex. (English) Zbl 1512.76023 Commun. Partial Differ. Equations 48, No. 1, 54-85 (2023). Reviewer: Fatma Gamze Duzgun (Ankara) MSC: 76B47 76B03 35Q31 PDFBibTeX XMLCite \textit{K. Choi} and \textit{I.-J. Jeong}, Commun. Partial Differ. Equations 48, No. 1, 54--85 (2023; Zbl 1512.76023) Full Text: DOI arXiv
Khesin, Boris; Misiołek, Gerard; Shnirelman, Alexander Geometric hydrodynamics in open problems. (English) Zbl 1509.35198 Arch. Ration. Mech. Anal. 247, No. 2, Paper No. 15, 43 p. (2023). MSC: 35Q31 35Q35 76-02 76B03 76N10 76U60 58D05 35A15 35A20 35A21 35A01 35A02 35B41 35B65 PDFBibTeX XMLCite \textit{B. Khesin} et al., Arch. Ration. Mech. Anal. 247, No. 2, Paper No. 15, 43 p. (2023; Zbl 1509.35198) Full Text: DOI arXiv
Elgindi, Tarek M.; Jeong, In-Jee On singular vortex patches. I: Well-posedness issues. (English) Zbl 1508.76028 Memoirs of the American Mathematical Society 1400. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-5682-5/pbk; 978-1-4704-7401-0/ebook). v, 89 p. (2023). MSC: 76B47 76B03 35Q31 PDFBibTeX XMLCite \textit{T. M. Elgindi} and \textit{I.-J. Jeong}, On singular vortex patches. I: Well-posedness issues. Providence, RI: American Mathematical Society (AMS) (2023; Zbl 1508.76028) Full Text: DOI arXiv
Jiu, Quansen; Li, You; Zhang, Wanwan Global well-posedness to the two-dimensional incompressible vorticity equation in the half plane. (English) Zbl 1498.35409 J. Math. Anal. Appl. 518, No. 1, Article ID 126684, 33 p. (2023). MSC: 35Q31 76B03 35A01 35A02 PDFBibTeX XMLCite \textit{Q. Jiu} et al., J. Math. Anal. Appl. 518, No. 1, Article ID 126684, 33 p. (2023; Zbl 1498.35409) Full Text: DOI arXiv
Hmidi, Taoufik; Houamed, Haroune; Zerguine, Mohamed Rigidity aspects of singular patches in stratified flows. (English) Zbl 1501.35316 Tunis. J. Math. 4, No. 3, 465-557 (2022). MSC: 35Q35 76B03 76B70 76D05 35Q31 35A01 35A02 PDFBibTeX XMLCite \textit{T. Hmidi} et al., Tunis. J. Math. 4, No. 3, 465--557 (2022; Zbl 1501.35316) Full Text: DOI arXiv
Córdoba, Diego; Martínez-Zoroa, Luis Non existence and strong ill-posedness in \(C^k\) and Sobolev spaces for SQG. (English) Zbl 1504.35566 Adv. Math. 407, Article ID 108570, 74 p. (2022). MSC: 35Q86 86A05 35A01 35R25 PDFBibTeX XMLCite \textit{D. Córdoba} and \textit{L. Martínez-Zoroa}, Adv. Math. 407, Article ID 108570, 74 p. (2022; Zbl 1504.35566) Full Text: DOI arXiv
Beekie, Rajendra; Friedlander, Susan; Vicol, Vlad On Moffatt’s magnetic relaxation equations. (English) Zbl 1508.35058 Commun. Math. Phys. 390, No. 3, 1311-1339 (2022). MSC: 35Q35 76B47 76B03 76W05 35A01 35A02 PDFBibTeX XMLCite \textit{R. Beekie} et al., Commun. Math. Phys. 390, No. 3, 1311--1339 (2022; Zbl 1508.35058) Full Text: DOI arXiv
Jolly, Michael S.; Kumar, Anuj; Martinez, Vincent R. On local well-posedness of logarithmic inviscid regularizations of generalized SQG equations in borderline Sobolev spaces. (English) Zbl 1496.76161 Commun. Pure Appl. Anal. 21, No. 1, 101-120 (2022). Reviewer: Gaston Vergara-Hermosilla (Dublin) MSC: 76U60 35Q35 PDFBibTeX XMLCite \textit{M. S. Jolly} et al., Commun. Pure Appl. Anal. 21, No. 1, 101--120 (2022; Zbl 1496.76161) Full Text: DOI arXiv
Elgindi, Tarek Finite-time singularity formation for \(C^{1,\alpha}\) solutions to the incompressible Euler equations on \(\mathbb{R}^3\). (English) Zbl 1492.35199 Ann. Math. (2) 194, No. 3, 647-727 (2021). Reviewer: Ming Mei (Montreal) MSC: 35Q31 35B40 35B35 35B45 35B20 PDFBibTeX XMLCite \textit{T. Elgindi}, Ann. Math. (2) 194, No. 3, 647--727 (2021; Zbl 1492.35199) Full Text: DOI arXiv
Elgindi, Tarek M.; Jeong, In-Jee The incompressible Euler equations under octahedral symmetry: singularity formation in a fundamental domain. (English) Zbl 1496.35297 Adv. Math. 393, Article ID 108091, 63 p. (2021). MSC: 35Q31 76B03 76M60 35B44 35B45 35B06 35A01 35A02 PDFBibTeX XMLCite \textit{T. M. Elgindi} and \textit{I.-J. Jeong}, Adv. Math. 393, Article ID 108091, 63 p. (2021; Zbl 1496.35297) Full Text: DOI arXiv
Jeong, In-Jee Loss of regularity for the 2D Euler equations. (English) Zbl 1493.76011 J. Math. Fluid Mech. 23, No. 4, Paper No. 95, 11 p. (2021). Reviewer: Song Jiang (Beijing) MSC: 76B03 35Q31 PDFBibTeX XMLCite \textit{I.-J. Jeong}, J. Math. Fluid Mech. 23, No. 4, Paper No. 95, 11 p. (2021; Zbl 1493.76011) Full Text: DOI arXiv
Jolly, Michael S.; Kumar, Anuj; Martinez, Vincent R. On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces. (English) Zbl 1479.35866 Commun. Math. Phys. 387, No. 1, 551-596 (2021). MSC: 35Q86 35Q35 76U60 35B65 35K59 35A01 35A02 86A05 PDFBibTeX XMLCite \textit{M. S. Jolly} et al., Commun. Math. Phys. 387, No. 1, 551--596 (2021; Zbl 1479.35866) Full Text: DOI arXiv
Jeong, In-Jee; Yoneda, Tsuyoshi Vortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equations. (English) Zbl 1479.35617 Math. Ann. 380, No. 3-4, 2041-2072 (2021). MSC: 35Q30 76D17 76D05 PDFBibTeX XMLCite \textit{I.-J. Jeong} and \textit{T. Yoneda}, Math. Ann. 380, No. 3--4, 2041--2072 (2021; Zbl 1479.35617) Full Text: DOI arXiv
Chae, Dongho; Wolf, Jörg The Euler equations in a critical case of the generalized Campanato space. (English) Zbl 1458.35308 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 38, No. 2, 201-241 (2021). MSC: 35Q31 76B03 35B44 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 38, No. 2, 201--241 (2021; Zbl 1458.35308) Full Text: DOI arXiv
Hieber, Matthias; Nguyen, Thieu Huy Stability and periodicity of solutions to the Oldroyd-B model on exterior domains. (English) Zbl 1458.76006 Rend. Ist. Mat. Univ. Trieste 52, 113-129 (2020). MSC: 76A10 35Q35 PDFBibTeX XMLCite \textit{M. Hieber} and \textit{T. H. Nguyen}, Rend. Ist. Mat. Univ. Trieste 52, 113--129 (2020; Zbl 1458.76006) Full Text: DOI Link
Elgindi, Tarek M.; Jeong, In-Jee Finite-time singularity formation for strong solutions to the axi-symmetric \(3D\) Euler equations. (English) Zbl 1436.35055 Ann. PDE 5, No. 2, Paper No. 16, 51 p. (2019). MSC: 35B44 35A20 35Q31 35B07 PDFBibTeX XMLCite \textit{T. M. Elgindi} and \textit{I.-J. Jeong}, Ann. PDE 5, No. 2, Paper No. 16, 51 p. (2019; Zbl 1436.35055) Full Text: DOI arXiv
Elgindi, Tarek M. Sharp \(L^{p}\) estimates for singular transport equations. (English) Zbl 1391.35084 Adv. Math. 329, 1285-1306 (2018). MSC: 35B45 PDFBibTeX XMLCite \textit{T. M. Elgindi}, Adv. Math. 329, 1285--1306 (2018; Zbl 1391.35084) Full Text: DOI arXiv
Misiołek, Gerard; Yoneda, Tsuyoshi Continuity of the solution map of the Euler equations in Hölder spaces and weak norm inflation in Besov spaces. (English) Zbl 1388.35160 Trans. Am. Math. Soc. 370, No. 7, 4709-4730 (2018). MSC: 35Q35 35B30 PDFBibTeX XMLCite \textit{G. Misiołek} and \textit{T. Yoneda}, Trans. Am. Math. Soc. 370, No. 7, 4709--4730 (2018; Zbl 1388.35160) Full Text: DOI arXiv
Gérard, Patrick; Koch, Herbert The cubic Szegő flow at low regularity. (English) Zbl 1475.35434 Sémin. Laurent Schwartz, EDP Appl. 2016-2017, Exp. No. 14, 14 p. (2017). MSC: 35S05 37K15 47B35 PDFBibTeX XMLCite \textit{P. Gérard} and \textit{H. Koch}, Sémin. Laurent Schwartz, EDP Appl. 2016--2017, Exp. No. 14, 14 p. (2017; Zbl 1475.35434) Full Text: DOI
Jeong, In-Jee; Pausader, Benoit Discrete Schrödinger equation and ill-posedness for the Euler equation. (English) Zbl 1366.35121 Discrete Contin. Dyn. Syst. 37, No. 1, 281-293 (2017). Reviewer: Georg V. Jaiani (Tbilisi) MSC: 35Q31 76D03 35R25 PDFBibTeX XMLCite \textit{I.-J. Jeong} and \textit{B. Pausader}, Discrete Contin. Dyn. Syst. 37, No. 1, 281--293 (2017; Zbl 1366.35121) Full Text: DOI
Hsu, P.-Y.; Notsu, H.; Yoneda, T. A local analysis of the axisymmetric Navier-Stokes flow near a saddle point and no-slip flat boundary. (English) Zbl 1462.76006 J. Fluid Mech. 794, 444-459 (2016). MSC: 76A02 76D05 PDFBibTeX XMLCite \textit{P. Y. Hsu} et al., J. Fluid Mech. 794, 444--459 (2016; Zbl 1462.76006) Full Text: DOI arXiv
Misiołek, Gerard; Yoneda, Tsuyoshi Local ill-posedness of the incompressible Euler equations in \(C^1\) and \(B^1_{\infty,1}\). (English) Zbl 1336.35280 Math. Ann. 364, No. 1-2, 243-268 (2016); erratum ibid. 363, No. 3–4, 1399–1400 (2015). Reviewer: Piotr Biler (Wrocław) MSC: 35Q31 35B30 35A01 PDFBibTeX XMLCite \textit{G. Misiołek} and \textit{T. Yoneda}, Math. Ann. 364, No. 1--2, 243--268 (2016; Zbl 1336.35280) Full Text: DOI arXiv
Bourgain, Jean; Li, Dong Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces. (English) Zbl 1480.35316 Geom. Funct. Anal. 25, No. 1, 1-86 (2015). MSC: 35Q31 35B30 35R25 PDFBibTeX XMLCite \textit{J. Bourgain} and \textit{D. Li}, Geom. Funct. Anal. 25, No. 1, 1--86 (2015; Zbl 1480.35316) Full Text: DOI arXiv