The Cauchy problem for the compressible Navier–Stokes equations in the Lp-framework Original Research Article

The global in time existence of regular solutions to the compressible Navier–Stokes equations in the whole space is obtained. The solutions are close to nontrivial equilibrium solutions. Moreover, the result is sharp in the Lp-framework, the velocity of the fluid belongs to Wr2,1 and the initial density to Wr1 with r>3.