Unique solvability for the density-dependent Navier-Stokes equations

초록

In this paper we consider the incompressible Navier-Stokes equations with a density-dependent viscosity in a bounded domain Omega of R-n (n = 2, 3). We prove the local existence of unique strong solutions for all initial data satisfying a natural compatibility condition. This condition is also necessary for a very general initial data. Moreover, we provide a blow-up criterion for the regularity of the strong solution. For these results, the initial density need not be strictly positive. It may vanish in an open subset of Omega. (C) 2004 Elsevier Ltd. All rights reserved.

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