Journal
MATHEMATISCHE ANNALEN
Volume -, Issue -, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00208-023-02621-x
Keywords
35Q35; 35B25; 76N10
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In this paper, the compressible Navier-Stokes system around constant equilibrium states is studied. It is proven that there exists a unique global solution for arbitrarily large initial data in the scaling critical Besov space, provided that the Mach number is sufficiently small and the incompressible part of the initial velocity generates the global solution of the incompressible Navier-Stokes equation. Furthermore, the low Mach number limit is considered, and it is shown that the compressible solution converges to the solution of the incompressible Navier-Stokes equation in certain space time norms.
In this paper, we consider the compressible Navier-Stokes system around the constant equilibrium states and prove the existence of a unique global solution for arbitrarily large initial data in the scaling critical Besov space provided that the Mach number is sufficiently small, and the incompressible part of the initial velocity generates the global solution of the incompressible Navier-Stokes equation. Moreover, we consider the low Mach number limit and show that the compressible solution converges to the solution of the incompressible Navier-Stokes equation in some space time norms.
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