Proves orbital stability of vortex patch minimizers for 2D Euler equations in domains with weak finite volume condition and in arbitrary-width strips by extending variational methods with Green's function comparison and concentration-compactness.
Stability of vortex quadrupoles with odd-odd sym- metry
3 Pith papers cite this work. Polarity classification is still indexing.
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In the odd symmetric half-plane setting, every compactly supported nonnegative initial vorticity admits an arbitrarily small smooth nonnegative perturbation that forces linear-in-time filamentation for the 2D Euler flow.
Multiple almost circular concentrated vortices in the 2D Euler equations remain concentrated over long time scales if they stay separated, supported by a new stability estimate for the logarithmic interaction energy.
citing papers explorer
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Stability of Vortex Patches in Channels
Proves orbital stability of vortex patch minimizers for 2D Euler equations in domains with weak finite volume condition and in arbitrary-width strips by extending variational methods with Green's function comparison and concentration-compactness.
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Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane
In the odd symmetric half-plane setting, every compactly supported nonnegative initial vorticity admits an arbitrarily small smooth nonnegative perturbation that forces linear-in-time filamentation for the 2D Euler flow.
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Long time confinement of multiple concentrated vortices
Multiple almost circular concentrated vortices in the 2D Euler equations remain concentrated over long time scales if they stay separated, supported by a new stability estimate for the logarithmic interaction energy.