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March/April 2009 The nonlinear Hodge-Navier-Stokes equations in Lipschitz domains
Marius Mitrea, Sylvie Monniaux
Differential Integral Equations 22(3/4): 339-356 (March/April 2009). DOI: 10.57262/die/1356019778


We investigate the Navier-Stokes equations in a suitable functional setting, in a three-dimensional bounded Lipschitz domain $\Omega$, equipped with ``free boundary'' conditions. In this context, we employ the Fujita-Kato method and prove the existence of a local mild solution. Our approach makes essential use of the properties of the Hodge-Laplacian in Lipschitz domains.


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Marius Mitrea. Sylvie Monniaux. "The nonlinear Hodge-Navier-Stokes equations in Lipschitz domains." Differential Integral Equations 22 (3/4) 339 - 356, March/April 2009.


Published: March/April 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35412
MathSciNet: MR2492825
Digital Object Identifier: 10.57262/die/1356019778

Primary: 35A15 , 35Q10 , 76D05

Rights: Copyright © 2009 Khayyam Publishing, Inc.

Vol.22 • No. 3/4 • March/April 2009
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