Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition

Pages: 1537 - 1564, Volume 14, Issue 4, November 2010

doi:10.3934/dcdsb.2010.14.1537       Abstract        Full Text (344.8K)       Related Articles

Jean-Pierre Raymond - Université de Toulouse & CNRS, Institut de Mathématiques, UMR 5219, 31062 Toulouse Cedex 9, France (email)

Abstract: 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:  Navier-Stokes equations, nonhomogeneous divergence condition, nonhomogeneous Dirichlet boundary condition.
Mathematics Subject Classification:  Primary: 35Q30, 76D05, 76D03; Secondary: 76D07.

Received: September 2009;      Revised: February 2010;      Published: August 2010.