Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition

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November 2010, 14(4): 1537-1564. doi: 10.3934/dcdsb.2010.14.1537

Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition

1.	Université de Toulouse & CNRS, Institut de Mathématiques, UMR 5219, 31062 Toulouse Cedex 9

Received September 2009 Revised February 2010 Published August 2010

Abstract
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In this paper, we study the existence and regularity of solutions to the Stokes and Oseen equations with a nonhomogeneous divergence condition. We also prove the existence of global weak solutions to the 3D Navier-Stokes equations when the divergence is not equal to zero. These equations intervene in control problems for the Navier-Stokes equations and in fluid-structure interaction problems.

Keywords: nonhomogeneous divergence condition, nonhomogeneous Dirichlet boundary condition., Navier-Stokes equations.

Mathematics Subject Classification: Primary: 35Q30, 76D05, 76D03; Secondary: 76D0.

Citation: Jean-Pierre Raymond. Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1537-1564. doi: 10.3934/dcdsb.2010.14.1537

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