Stability in 𝐿¹ of circular vortex patches

DOI10.1090/S0002-9939-09-10048-5zbMath1181.35201arXiv0909.4111MaRDI QIDQ3648181

Thomas C. Sideris, Luis Vega

Publication date: 24 November 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.4111

zbMATH Keywords

circular vortex patchesplanar incompressible and ideal fluid flow

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Vortex flows for incompressible inviscid fluids (76B47) Hydrodynamic stability (76E99)

Related Items

Stability of radially symmetric, monotone vorticities of 2D Euler equations, Stability of Lamb dipoles, Vortices on Closed Surfaces, Nonlinear stability for stationary helical vortices, Stability of Hill's spherical vortex, On singular vortex patches, II: Long-time dynamics, 2D Euler equation on the strip: Stability of a rectangular patch, Growth of perimeter for vortex patches in a bulk, On the estimate of distance traveled by a particle in a disk-like vortex patch, Strong continuity for the 2D Euler equations, Symmetry in stationary and uniformly rotating solutions of active scalar equations, Stability and instability of Kelvin waves, Stability of monotone, nonnegative, and compactly supported vorticities in the half cylinder and infinite perimeter growth for patches

Cites Work

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• Nonlinear stability bounds for inviscid, two-dimensional, parallel or circular flows with monotonic vorticity, and the analogous three-dimensional quasi-geostrophic flows
• Vortex Dynamics