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

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

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Autor: Gancedo García, Francisco
García Juárez, Eduardo Miguel
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2018
Publicado en: Archive for Rational Mechanics and Analysis, 229 (1), 339-360.
Tipo de documento: Artículo
Resumen: 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.
Tamaño: 231.4Kb
Formato: PDF

URI: https://hdl.handle.net/11441/70963

DOI: 10.1007/s00205-018-1218-4

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