The incompressible limits of compressible Navier-Stokes equations in the whole space with general initial data

Abstract

It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists. The proof of the result relies on the new modulated energy functional and the Strichartz’s estimate of linear wave equation.

Keywords

Compressible Navier-Stokes equations / Incompressible Navier-Stokes equations / Low Mach number limit / Modulated energy functional / Strichartz’s estimate

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