Abstract
The previous results on a global in time existence or stability have based on the local time existence in anisotropic Sobolev-Slobodetski spacesW22+r, 1+r/2, which are obtained by energy method for weak norm estimates, and by linear theory for higher norm estimates. On the other hand, in the paper of B.J. Jin and M. Padula [2], the global in time existence and stability have been obtained by purely Energy method, where the regularity class is different from anisotropic Sobolev-Slobodetski spacesW22+r, 1+r/2. We construct solution local in time of viscous compressible Navier-Stokes equations in a moving domain with free surface, via Galerkin method for the solution of linearized problem and, via iterative procedure for the solution of the nonlinear problem. With this method we obtain local in time solution whose regularity class is the same as the one in [2].
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