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Global regularity of 2D density patches for inhomogeneous Navier-Stokes

 

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Opened Access Global regularity of 2D density patches for inhomogeneous Navier-Stokes
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Author: Gancedo García, Francisco
García Juárez, Eduardo Miguel
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2018
Published in: Archive for Rational Mechanics and Analysis, 229 (1), 339-360.
Document type: Article
Abstract: This paper is about Lions’ open problem on density patches: whether inhomogeneous incompressible Navier-Stokes equations preserve the initial regularity of the free boundary given by density patches. Using classical Sobolev spaces for the velocity, we first establish the propagation of C1+γ regularity with 0 < γ < 1 in the case of positive density. Furthermore, we go beyond to show the persistence of a geometrical quantity such as the curvature. In addition, we obtain a proof for C2+γ regularity.
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URI: https://hdl.handle.net/11441/70963

DOI: 10.1007/s00205-018-1218-4

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