Singularity formation in the incompressible Euler equation in finite and infinite time
TD Drivas, TM Elgindi - EMS Surveys in Mathematical Sciences, 2023 - ems.press
Some classical and recent results on the Euler equations governing perfect (incompressible
and inviscid) fluid motion are collected and reviewed, with some small novelties scattered …
and inviscid) fluid motion are collected and reviewed, with some small novelties scattered …
Twisting in hamiltonian flows and perfect fluids
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional
annular surfaces. This notion of stability is designed to capture the sustained twisting of …
annular surfaces. This notion of stability is designed to capture the sustained twisting of …
The stabilizing effect of temperature and magnetic field on a 2D magnetic Bénard fluids
S Lai, L Shen, X Ye, X Zhao - Journal of Differential Equations, 2024 - Elsevier
In this paper we study the stability of a special magnetic Bénard system near equilibrium,
where there exists Laplacian magnetic diffusion and temperature dam** but the velocity …
where there exists Laplacian magnetic diffusion and temperature dam** but the velocity …
Stability and instability of Kelvin waves
The m-waves of Kelvin are uniformly rotating patch solutions of the 2D Euler equations with
m-fold rotational symmetry for m≥ 2. For Kelvin waves sufficiently close to the disc, we prove …
m-fold rotational symmetry for m≥ 2. For Kelvin waves sufficiently close to the disc, we prove …
Stability and large-time behavior on 3D incompressible MHD equations with partial dissipation near a background magnetic field
H Lin, J Wu, Y Zhu - arxiv preprint arxiv:2210.16600, 2022 - arxiv.org
Physical experiments and numerical simulations have observed a remarkable stabilizing
phenomenon: a background magnetic field stabilizes and damps electrically conducting …
phenomenon: a background magnetic field stabilizes and damps electrically conducting …
Regular and Singular Steady States of the 2D Incompressible Euler Equations near the Bahouri–Chemin Patch
TM Elgindi, Y Huang - Archive for Rational Mechanics and Analysis, 2025 - Springer
We consider steady states of the two-dimensional incompressible Euler equations
on\({\mathbb {T}}^ 2\) and construct smooth and singular steady states around a particular …
on\({\mathbb {T}}^ 2\) and construct smooth and singular steady states around a particular …
Well-posedness for Ohkitani model and long-time existence for surface quasi-geostrophic equations
We consider the Cauchy problem for the logarithmically singular surface quasi-geostrophic
(SQG) equation, introduced by Ohkitani, $$\partial_t\theta-\nabla^\perp\log (10+ …
(SQG) equation, introduced by Ohkitani, $$\partial_t\theta-\nabla^\perp\log (10+ …
On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex
The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler
equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis …
equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis …
Stability of Monotone, Nonnegative, and Compactly Supported Vorticities in the Half Cylinder and Infinite Perimeter Growth for Patches
We consider the incompressible Euler equations in the half cylinder R> 0× T. In this domain,
any vorticity which is independent of x 2 defines a stationary solution. We prove that such a …
any vorticity which is independent of x 2 defines a stationary solution. We prove that such a …
Stability of vortex quadrupoles with odd-odd symmetry
For the 2D incompressible Euler equations, we establish global-in-time ($ t\in\mathbb {R} $)
stability of vortex quadrupoles satisfying odd symmetry with respect to both axes …
stability of vortex quadrupoles satisfying odd symmetry with respect to both axes …