Well‐posedness for compressible Euler equations with physical vacuum singularity

By Juhi Jang, Nader Masmoudi. 2008

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An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristic speeds u ± c coincide and have unbounded spatial derivative since c behaves like x1/2 close to the boundary. In this paper, we overcome this difficulty by presenting a new formulation and new energy spaces. We establish the local‐in‐time well‐posedness of one‐dimensional compressible Euler equations for isentropic flows with the physical vacuum singularity in some spaces adapted to the singularity. © 2009 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ee67f379eabfa9ccb15f48c1ae0fc9ba211d183c

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In Applied Mathematics

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

Uniform Regularity for the Navier–Stokes Equation with Navier Boundary Condition (2010, unknown): “The use of conormal Sobolev spaces has a long history in (hyperbolic) boundary value problems, we refer for example to [14], [36], [2], [13, 17] and references therein.”
Well‐posedness in smooth function spaces for moving‐boundary 1‐D compressible euler equations in physical vacuum (2009, background): “I /-norm, an example of the type of bound that is proved for the rescaled velocity field in [6] is the following: kdvk0 C kdvxk0 C kdvxx C 2vxk0 C kdvxxx C 2vxx 2d vxk0 C kdvxxxx C 4vxxx 4d vxxk0 <1: (1.”