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  and the contraction mapping principle.
Published February 28, 2007.
Math Subject Classifications: 35Q30, 76D05.
Key Words: Navier-Stokes equations; moving boundary; maximal regularity.
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| Jürgen Saal |
Department of Mathematics and Statistics
University of Konstanz
Box D 187, 78457 Konstanz, Germany
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