A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows

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URI: https://hdl.handle.net/10902/29400
ISSN: 0002-9939
ISSN: 1088-6826
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Autoría
Geng, Zhiyuan; Granero Belinchón, RafaelAutoridad Unican
Fecha
2023
Derechos
© American Mathematical Society. First published in Proceedings of the American Mathematical Society in volume 151 (2), 2023, published by the American Mathematical Society
Publicado en
Proceedings of the American Mathematical Society, 2023, 151(2), 707-722
Editorial
American Mathematical Society
Resumen/Abstract
In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of the Euler equations, also the tangential velocity at the interface are sufficiently smooth, the depth cannot vanish in finite time. This results holds regardless of gravity and surface tension effects or, if applicable, the stratification in multiphase flows.
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