Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 15 (2007), pp. 365-375. 

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

Author: Juergen Saal (Univ. of Konstanz, Germany)
 
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.

Published February 28, 2007.
Math Subject Classifications: 35Q30, 76D05.
Key Words: Navier-Stokes equations; moving boundary; maximal regularity.