$Velocity blow-up in $C^1\cap H^2$ for the 2D Euler equations$

Velocity blow-up in $C^1\cap H^2$ for the 2D Euler equations

We give a vorticity-dynamical proof of $C^1\cap H^2$-illposedness of the 2D Euler equations. Our construction shows that the unique Yudovich solution escapes both $C^1$ and $H^2$ instantaneously.

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Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org 2022-11
Hauptverfasser:	Min, Jun Jo, Kim, Junha
Format:	Artikel
Sprache:	eng
Schlagworte:	Euler-Lagrange equation Mathematical analysis Vorticity
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We give a vorticity-dynamical proof of $C^1\cap H^2$-illposedness of the 2D Euler equations. Our construction shows that the unique Yudovich solution escapes both $C^1$ and $H^2$ instantaneously.
ISSN:	2331-8422

Zusammenfassung:	We give a vorticity-dynamical proof of \(C^1\cap H^2\)-illposedness of the 2D Euler equations. Our construction shows that the unique Yudovich solution escapes both \(C^1\) and \(H^2\) instantaneously.
ISSN:	2331-8422

Velocity blow-up in \(C^1\cap H^2\) for the 2D Euler equations