Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition
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.
Received: September 2009; Revised: February 2010; Published: August 2010.
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