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.

中文翻译：

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等熵可压缩Navier–Stokes方程在真空中的局部适定性

在本文中，证明了等熵可压缩Navier–Stokes方程的Cauchy问题的强解的局部适定性，并允许初始数据具有真空。本文的主要贡献在于，在不假设初始数据具有任何相容性条件的情况下建立了适定性，这在很多关于存在真空的可压缩Navier-Stokes方程的适定性之前被广泛使用。