Various boundary conditions for Navier-Stokes equations in bounded Lipschitz domains

Sylvie Monniaux

doi:10.3934/dcdss.2013.6.1355

Article Contents

2013, Volume 6, Issue 5: 1355-1369. Doi: 10.3934/dcdss.2013.6.1355

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Various boundary conditions for Navier-Stokes equations in bounded Lipschitz domains

Sylvie Monniaux^1,

1.
Sylvie Monniaux - LATP CMI Université Aix-Marseille, 39 rue Frédéric Joliot-Curie, 13453 Marseille Cedex 13

Received: October 31, 2011

Revised: November 30, 2011

Published: September 2013

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Abstract

We present here different boundary conditions for the Navier-Stokes equations in bounded Lipschitz domains in $\mathbb{R}^3$, such as Dirichlet, Neumann or Hodge boundary conditions. We first study the linear Stokes operator associated to the boundary conditions. Then we show how the properties of the operator lead to local solutions or global solutions for small initial data.

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Mathematics Subject Classification: Primary: 35Q30, 35Q35, 35J25.

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References

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