The Cauchy problem for the compressible Navier-Stokes equations in the \(L_p\)-framework
The author considers compressible Navier-Stokes equations describing the motion of isentropic viscous fluid in the whole space. Using a priori time-independent energy estimates in anisotropic Sobolev spaces, the global in time existence of regular solutions is proved under some smallness assumptions. These solutions are close to nontrivial equilibrium solutions. The result is shown to be sharp in the \(L_p\)-framework.
scientific article; zbMATH DE number 1880014