Abstract.
We consider the evolutionary Navier–Stokes equations with a Navier slip-type boundary condition, and study the convergence of the solutions, as the viscosity goes to zero, to the solution of the Euler equations under the zero-flux boundary condition. We obtain quite sharp results in the 2-D and 3-D cases. However, in the 3-D case, we need to assume that the boundary is flat.
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da Veiga, H.B., Crispo, F. Sharp Inviscid Limit Results under Navier Type Boundary Conditions. An Lp Theory. J. Math. Fluid Mech. 12, 397–411 (2010). https://doi.org/10.1007/s00021-009-0295-4
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DOI: https://doi.org/10.1007/s00021-009-0295-4