Strong solutions of the Navier-Stokes equations for isentropic compressible fluids.(English)Zbl 1022.35037

Summary: We study strong solutions of the isentropic compressible Navier-Stokes equations in a domain $$\Omega\subset\mathbb{R}^{3}$$. We first prove the local existence of unique strong solutions provided that the initial data $$\rho_0$$ and $$u_0$$ satisfy a natural compatibility condition. The important point in this paper is that we allow the initial vacuum: the initial density may vanish in an open subset of $$\Omega$$. We then prove a new uniqueness result and stability result. Our results are valid for unbounded domains as well as bounded ones.

MSC:

 35Q30 Navier-Stokes equations 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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References:

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