Two-dimensional incompressible ideal flows in a noncylindrical material domain

Flavia Z. Fernandes; Milton C. Lopes Filho

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Two-dimensional incompressible ideal flows in a noncylindrical material domain

Flavia Z. Fernandes·Milton C. Lopes Filho

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Abstract

The purpose of this work is to prove existence of a weak solution of the two dimensional incompressible Euler equations on a noncylindrical domain consisting of a smooth, bounded, connected and simply connected domain undergoing a prescribed motion. We prove existence of a weak solution for initial vorticity in $L^p$, for $p>1$. This work complements a similar result by C. He and L. Hsiao, who proved existence assuming that the flow velocity is tangent to the moving boundary, see [JDE v. 163 (2000) 265--291].

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Flavia Z. Fernandes, Milton C. Lopes Filho. 2007-02-01. Two-dimensional incompressible ideal flows in a noncylindrical material domain. https://arxiv.org/abs/math/0702026

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