Journal
MANUSCRIPTA MATHEMATICA
Volume 120, Issue 1, Pages 91-129Publisher
SPRINGER
DOI: 10.1007/s00229-006-0637-y
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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.
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