Nonlinear stability of sinusoidal Euler flows on a flat two-torus

Nonlinear stability of sinusoidal Euler flows on a flat two-torus

Sinusoidal flows are an important class of explicit stationary solutions of the two-dimensional incompressible Euler equations on a flat torus. For such flows, the steam functions are eigenfunctions of the negative Laplacian. In this paper, we prove that any sinusoidal flow related to some least eig...

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Veröffentlicht in:arXiv.org 2022-10
Hauptverfasser: Wang, Guodong, Zuo, Bijun
Format: Artikel
Sprache:eng
Schlagworte:
Eigenvectors
Euler-Lagrange equation
Fluid flow
Incompressible flow
Mathematical analysis
Sine waves
Stability
Toruses
Translations
Vorticity
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Zusammenfassung:Sinusoidal flows are an important class of explicit stationary solutions of the two-dimensional incompressible Euler equations on a flat torus. For such flows, the steam functions are eigenfunctions of the negative Laplacian. In this paper, we prove that any sinusoidal flow related to some least eigenfunction is, up to phase translations, nonlinearly stable under \(L^p\) norm of the vorticity for any \(1
ISSN:2331-8422