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arXiv · 1201.1986

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

Lizhen Wang·Zhouping Xin·Aibin Zang
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Abstract

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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Lizhen Wang, Zhouping Xin, Aibin Zang. 2012-01-10. Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition. https://doi.org/10.1007/s00021-012-0103-4

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