STRONG SOLUTIONS FOR THE NAVIER-STOKES EQUATIONS ON BOUNDED AND UNBOUNDED DOMAINS WITH A MOVING BOUNDARY

It is proved under mild regularity assumptions on the data that the Navier-Stokes equations in bounded and unbounded noncylindrical regions admit a unique local-in-time strong solution. The result is based on maximal regularity estimates for the in spatial regions with a moving boundary obtained in (16) and the contraction mapping principle.