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Well-posedness of the
hydrostatic Navier–Stokes equations
David Gérard-Varet, Nader Masmoudi and Vlad Vicol |
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Vol. 13 (2020), No. 5, 1417–1455
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Abstract |
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We address the local well-posedness of the hydrostatic Navier–Stokes equations. These equations, sometimes called reduced Navier–Stokes/Prandtl, appear as a formal limit of the Navier–Stokes system in thin domains, under certain constraints on the aspect ratio and the Reynolds number. It is known that without any structural assumption on the initial data, real-analyticity is both necessary and sufficient for the local well-posedness of the system. In this paper we prove that for convex initial data, local well-posedness holds under simple Gevrey regularity. |
Keywords
fluid mechanics, Navier–Stokes equations
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Mathematical Subject Classification 2010
Primary: 35Q30
Secondary: 35Q35
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Milestones
Received: 12 April 2018
Revised: 2 May 2019
Accepted: 11 June 2019
Published: 27 July 2020
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Authors |
| David Gérard-Varet | |
| Institut de Mathématiques de
Jussieu-Paris Rive Gauche Université Paris Diderot Institut Universitaire de France Paris France |
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| Nader Masmoudi | |
| Courant Institute of Mathematical
Sciences New York University New York United States |
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| Vlad Vicol | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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