Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition

Details Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition

2012-01-10

arxiv.org/abs/1201.1986v2

Mathematics

Analysis of PDEs

45pages

Scientific paper

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and $L^\infty((0,T)\times\o)$, where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.

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