On Classical Solutions of the Compressible Navier-stokes Equations with Nonnegative Initial Densities
نویسندگان
چکیده
We study the Navier-Stokes equations for compressible barotropic fluids in a bounded or unbounded domain Ω of R3. We first prove the local existence of solutions (ρ, u) in C([0, T∗]; (ρ∞+ H3(Ω))× (D1 0 ∩D3)(Ω)) 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 (ρ, u) is a classical solution in (0, T∗∗)× Ω 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 Ω.
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