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We prove the local well-posedness for the barotropic compressibleNavier-Stokes system on a moving domain, a motion of which is determined by agiven vector field ${\bf V}$, in a maximal $L_p-L_q$ regularity framework.Under additional smallness assumptions on the data we show that our solutionexists globally in time and satisfies a decay estimate. In particular, for theglobal well-posedness we don't require exponential decay or smallness of ${\bfV}$ in $L_p(L_q)$. However, we require exponential decay and smallness of itsderivatives.

Compressible Navier-Stokes system on a moving domain in the $L_p-L_q$ framework