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

By Lizhen Wang, Zhouping Xin, Aibin Zang. 2012

67 citations recorded by the source corpus.

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 R3. 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]; H1(Ω)) 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.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/6daa334c0ec335c2e9c20abdd4fdcad433c4ce6c

Citations in the corpus

• On the Inviscid Limit for the Compressible Navier–Stokes System in an Impermeable Bounded Domain (2012, unknown): “(i.e. [23, 22, 28, 2, 37]) use a strategy somehow related to the issue of weak-strong uniqueness, where one compares two solutions of the same equation, only one of which being smooth. In the results [23, 22, 28, 2, 37] there is also a comparison between a weak and a strong solution but the word “so”