Article
Global regularity of 2D density patches for inhomogeneous Navier-Stokes
Author/s | Gancedo García, Francisco
García Juárez, Eduardo Miguel |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2018 |
Deposit Date | 2018-03-14 |
Published in |
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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 ... 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. |
Project ID. | P12-FQM-2466
MTM2014-59488-P H2020-EU.1.1.-639227 |
Citation | Gancedo García, F. y García Juárez, E.M. (2018). Global regularity of 2D density patches for inhomogeneous Navier-Stokes. Archive for Rational Mechanics and Analysis, 229 (1), 339-360. |
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