On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities

초록

We study the Navier-Stokes equations for compressible barotropic fluids in a bounded or unbounded domain Omega of R-3. We first prove the local existence of solutions (rho, u) in C([ 0, T-*]; (rho(infinity) + H-3(Omega)) x (D-0(1) boolean AND D-3)(Omega)) under the assumption that the data satisfies a natural compatibility condition. Then deriving the smoothing effect of the velocity u in t > 0, we conclude that (rho, u) is a classical solution in ( 0, T-**) x Omega for some T**. (0, T*). For these results, the initial density needs not be bounded below away from zero and may vanish in an open subset (vacuum) of Omega.

키워드