On singular vortex patches, II: Long-time dynamics
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Publication:5125177
DOI10.1090/tran/8134zbMath1454.35265arXiv1909.13555OpenAlexW3006952923MaRDI QIDQ5125177
In-Jee Jeong, Tarek Mohamed Elgindi
Publication date: 5 October 2020
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1909.13555
Asymptotic behavior of solutions to PDEs (35B40) Periodic solutions to PDEs (35B10) Vortex flows for incompressible inviscid fluids (76B47) General theory of rotating fluids (76U05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
- Degenerate bifurcation of the rotating patches
- Bifurcation of rotating patches from Kirchhoff vortices
- Finite time singularity for the modified SQG patch equation
- Small scale creation for solutions of the incompressible two-dimensional Euler equation
- Existence of corotating and counter-rotating vortex pairs for active scalar equations
- Nonlinear stability of circular vortex patches
- Contour surgery: A topological reconnection scheme for extended integrations using contour dynamics
- On the evolution of nearly circular vortex patches
- Motions of vortex patches
- Wandering solutions of Euler's D-2 equation
- On the evolution of an angle in a vortex patch
- Uniformly rotating smooth solutions for the incompressible 2D Euler equations
- Global regularity for vortex patches
- Evolution of a cusp-type singularity in a vortex patch
- On the estimate of distance traveled by a particle in a disk-like vortex patch
- Finite-time singularity formation for strong solutions to the axi-symmetric \(3D\) Euler equations
- Boundary regularity of rotating vortex patches
- Stability in 𝐿¹ of circular vortex patches
- Vorticity and the mathematical theory of incompressible fluid flow
- Nonlinear stability bounds for inviscid, two-dimensional, parallel or circular flows with monotonic vorticity, and the analogous three-dimensional quasi-geostrophic flows
- The repeated filamentation of two-dimensional vorticity interfaces
- Wave and vortex dynamics on the surface of a sphere
- Evolution temporelle d'une poche de tourbillon singuliere
- Multiscale Approximation of Vortex Patches
- On singular vortex patches, II: Long-time dynamics
- Investigating Stability and Finding New Solutions in Conservative Fluid Flows Through Bifurcation Approaches
- Vortex Dynamics
- Global regularity and fast small-scale formation for Euler patch equation in a smooth domain
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