Strong solutions for the Navier-Stokes equations on bounded and unbounded domains with a moving boundary

Abstract

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.

Keywords

• Navier-Stokes equations
• moving boundary
• maximal regularity.