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Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum. (English) Zbl 1467.35242

Summary: In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial data being allowed to have vacuum. The main contribution of this paper is that the well-posedness is established without assuming any compatibility condition on the initial data, which was widely used before in many works concerning the well-posedness of compressible Navier-Stokes equations in the presence of vacuum.

MSC:

35Q30 Navier-Stokes equations
35D35 Strong solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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