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
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
Kiselev, Alexander; Yao, Yao Small scale formations in the incompressible porous media equation. (English) Zbl 1504.35336 Arch. Ration. Mech. Anal. 247, No. 1, Paper No. 1, 25 p. (2023). MSC: 35Q35 76S05 76D50 35B35 PDFBibTeX XMLCite \textit{A. Kiselev} and \textit{Y. Yao}, Arch. Ration. Mech. Anal. 247, No. 1, Paper No. 1, 25 p. (2023; Zbl 1504.35336) Full Text: DOI arXiv
Choi, Kyudong; Jeong, In-Jee Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole. (English) Zbl 1482.35162 Nonlinear Anal., Real World Appl. 65, Article ID 103470, 20 p. (2022). MSC: 35Q31 76B47 76B03 35Q35 35Q86 PDFBibTeX XMLCite \textit{K. Choi} and \textit{I.-J. Jeong}, Nonlinear Anal., Real World Appl. 65, Article ID 103470, 20 p. (2022; Zbl 1482.35162) 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
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
He, Siming; Kiselev, Alexander Small-scale creation for solutions of the SQG equation. (English) Zbl 1473.35579 Duke Math. J. 170, No. 5, 1027-1041 (2021). MSC: 35Q86 35Q35 76B03 86A10 35B44 PDFBibTeX XMLCite \textit{S. He} and \textit{A. Kiselev}, Duke Math. J. 170, No. 5, 1027--1041 (2021; Zbl 1473.35579) Full Text: DOI arXiv
Zlatoš, Andrej On the rate of merging of vorticity level sets for the 2D Euler equations. (English) Zbl 1403.35223 J. Nonlinear Sci. 28, No. 6, 2329-2341 (2018). MSC: 35Q31 PDFBibTeX XMLCite \textit{A. Zlatoš}, J. Nonlinear Sci. 28, No. 6, 2329--2341 (2018; Zbl 1403.35223) Full Text: DOI arXiv
Kiselev, Alexander; Yao, Yao; Zlatoš, Andrej Local regularity for the modified SQG patch equation. (English) Zbl 1371.35220 Commun. Pure Appl. Math. 70, No. 7, 1253-1315 (2017). MSC: 35Q35 35Q31 35Q86 35B65 86A05 76B03 PDFBibTeX XMLCite \textit{A. Kiselev} et al., Commun. Pure Appl. Math. 70, No. 7, 1253--1315 (2017; Zbl 1371.35220) Full Text: DOI arXiv
Kiselev, Alexander; Ryzhik, Lenya; Yao, Yao; Zlatoš, Andrej Finite time singularity for the modified SQG patch equation. (English) Zbl 1360.35159 Ann. Math. (2) 184, No. 3, 909-948 (2016). Reviewer: Alpár R. Mészáros (Los Angeles) MSC: 35Q31 35Q86 35B65 76B03 86A05 PDFBibTeX XMLCite \textit{A. Kiselev} et al., Ann. Math. (2) 184, No. 3, 909--948 (2016; Zbl 1360.35159) Full Text: DOI arXiv Link
Xu, Xiaoqian Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flow. (English) Zbl 1339.35251 J. Math. Anal. Appl. 439, No. 2, 594-607 (2016). MSC: 35Q35 76B03 PDFBibTeX XMLCite \textit{X. Xu}, J. Math. Anal. Appl. 439, No. 2, 594--607 (2016; Zbl 1339.35251) Full Text: DOI arXiv
Kiselev, Alexander; Zlatoš, Andrej Blow up for the 2D Euler equation on some bounded domains. (English) Zbl 1319.35174 J. Differ. Equations 259, No. 7, 3490-3494 (2015). MSC: 35Q31 35B44 35B65 PDFBibTeX XMLCite \textit{A. Kiselev} and \textit{A. Zlatoš}, J. Differ. Equations 259, No. 7, 3490--3494 (2015; Zbl 1319.35174) Full Text: DOI arXiv
Denisov, Sergey A. Double exponential growth of the vorticity gradient for the two-dimensional Euler equation. (English) Zbl 1315.35150 Proc. Am. Math. Soc. 143, No. 3, 1199-1210 (2015). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q31 35B45 76B47 PDFBibTeX XMLCite \textit{S. A. Denisov}, Proc. Am. Math. Soc. 143, No. 3, 1199--1210 (2015; Zbl 1315.35150) Full Text: DOI arXiv
Zlatoš, Andrej Exponential growth of the vorticity gradient for the Euler equation on the torus. (English) Zbl 1308.35194 Adv. Math. 268, 396-403 (2015). MSC: 35Q31 PDFBibTeX XMLCite \textit{A. Zlatoš}, Adv. Math. 268, 396--403 (2015; Zbl 1308.35194) Full Text: DOI arXiv
Kiselev, Alexander; Šverák, Vladimir Small scale creation for solutions of the incompressible two-dimensional Euler equation. (English) Zbl 1304.35521 Ann. Math. (2) 180, No. 3, 1205-1220 (2014). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q31 PDFBibTeX XMLCite \textit{A. Kiselev} and \textit{V. Šverák}, Ann. Math. (2) 180, No. 3, 1205--1220 (2014; Zbl 1304.35521) Full Text: DOI arXiv
Kuznetsov, E. A.; Naulin, V.; Nielsen, A. H.; Rasmussen, J. Juul Effects of sharp vorticity gradients in two-dimensional hydrodynamic turbulence. (English) Zbl 1182.76415 Phys. Fluids 19, No. 10, Paper No. 105110, 10 p. (2007). MSC: 76-XX PDFBibTeX XMLCite \textit{E. A. Kuznetsov} et al., Phys. Fluids 19, No. 10, Paper No. 105110, 10 p. (2007; Zbl 1182.76415) Full Text: DOI Link
Deryabin, Mikhail V.; Willatzen, Morten Flow acoustics and linearized equations for ideal barotropic fluid flows. (English) Zbl 1111.76049 J. Math. Phys. 47, No. 4, 043101, 12 p. (2006). MSC: 76Q05 76E99 76N15 PDFBibTeX XMLCite \textit{M. V. Deryabin} and \textit{M. Willatzen}, J. Math. Phys. 47, No. 4, 043101, 12 p. (2006; Zbl 1111.76049) Full Text: DOI
Ohkitani, Koji A survey on a class of exact solutions of the Navier-Stokes equations and a model for turbulence. (English) Zbl 1070.76012 Publ. Res. Inst. Math. Sci. 40, No. 4, 1267-1290 (2004). MSC: 76D05 76F02 76D17 PDFBibTeX XMLCite \textit{K. Ohkitani}, Publ. Res. Inst. Math. Sci. 40, No. 4, 1267--1290 (2004; Zbl 1070.76012) Full Text: DOI
Morgulis, Andrey; Yudovich, Victor Arnold’s method for asymptotic stability of steady inviscid incompressible flow through a fixed domain with permeable boundary. (English) Zbl 1080.76521 Chaos 12, No. 2, 356-371 (2002). MSC: 76E30 76B99 37N10 PDFBibTeX XMLCite \textit{A. Morgulis} and \textit{V. Yudovich}, Chaos 12, No. 2, 356--371 (2002; Zbl 1080.76521) Full Text: DOI