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Vanishing viscous limits for 3D Navier-Stokes equations with a Navier-slip boundary condition. (English) Zbl 1256.35068

Summary: 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 \(\mathbb R^3\). 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 \(L^\infty((0,T) \times \Omega)\), where \(T\) is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.

MSC:

35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
35D35 Strong solutions to PDEs
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