Differential and Integral Equations

The nonlinear Hodge-Navier-Stokes equations in Lipschitz domains

Marius Mitrea and Sylvie Monniaux

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Abstract

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.

Article information

Source
Differential Integral Equations Volume 22, Number 3/4 (2009), 339-356.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019778

Mathematical Reviews number (MathSciNet)
MR2492825

Zentralblatt MATH identifier
1240.35412

Subjects
Primary: 35Q10 76D05: Navier-Stokes equations [See also 35Q30] 35A15: Variational methods

Citation

Mitrea, Marius; Monniaux, Sylvie. The nonlinear Hodge-Navier-Stokes equations in Lipschitz domains. Differential Integral Equations 22 (2009), no. 3/4, 339--356. https://projecteuclid.org/euclid.die/1356019778.


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