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


On the zero-viscosity limit for 3D Navier-Stokes equations under slip boundary conditions

Pages: 205-217
Received: 25 February 2010   
Accepted: 7 April 2010
Mathematics Subject Classification (2000): 35Q30, 76D05, 76D09.

Keywords: Navier-Stokes equations, slip boundary conditions, zero-viscosity limit.

Abstract: In this survey article we consider the initial-boundary value problem for the three-dimensional Navier-Stokes equations with Navier boundary conditions and study the problem of convergence of the solutions, as the viscosity goes to zero, to the solution of the Euler equations. We present some strong convergence results, obtained in collaboration with H. Beirão da Veiga (see [4] and [5]), in the case where the region of motion is a bounded domain with flat boundaries.

[4] H. Beirão da Veiga and F. Crispo, Sharp Inviscid Limit Results under Navier Type Boundary Conditions. An Lp Theory, J. Math. Fluid Mech. 12 (2010) 397411, DOI: 10.1007/s00021-009-0295-4
[5] H. Beirão da Veiga and F. Crispo, Concerning the Wk,p-Inviscid Limit for 3-D Flows Under a Slip Boundary Condition, J. Math. Fluid Mech. (2009), DOI: 10.1007/s00021-009-0012-3

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