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Well‐posedness of Compressible Euler Equations in a Physical Vacuum
Author(s) -
Jang Juhi,
Masmoudi Nader
Publication year - 2015
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21517
Subject(s) - polytropic process , degenerate energy levels , euler equations , compressibility , boundary value problem , boundary (topology) , mathematics , euler system , physical system , physics , euler's formula , classical mechanics , mechanics , mathematical analysis , quantum mechanics
An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of a vacuum. In particular, physical vacuum, in which the boundary moves with a nontrivial finite normal acceleration, naturally arises in the study of the motion of gaseous stars or shallow water. Despite its importance, there are only a few mathematical results available near a vacuum. The main difficulty lies in the fact that the physical systems become degenerate along the vacuum boundary. In this paper, we establish the local‐in‐time well‐posedness of three‐dimensional compressible Euler equations for polytropic gases with a physical vacuum by considering the problem as a free boundary problem. © 2015 Wiley Periodicals, Inc.