Riv. Mat. Univ. Parma, Vol. 1, No. 1, 2010


Some results on the Navier-Stokes equations with Navier boundary conditions

Pages: 1-75
Received: 26 February 2010   
Accepted: 20 April 2010
Mathematics Subject Classification (2000): 35Q30, 76F65, 76D03, 76D09.

Keywords: Stokes equations, Navier-Stokes equations, existence, regularity, singular limits.

Abstract: I make an overview of some results concerning the Stokes and Navier-Stokes equations, supplemented with the Navier's type slip boundary conditions. I try to explain the interest for this problem, the main analytical results, and also the differences between the flat case and more general cases. Some recent results concerning the vanishing viscosity limits are also announced.

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