Inviscid limit on L ^p -based Sobolev conormal spaces for the 3D Navier-Stokes equations with the Navier-boundary conditions

We establish uniform bounds and the inviscid limit in Lp-based Sobolev conormal spaces for the solutions of the Navier-Stokes equations with the Navier-boundary conditions in the half-space. We extend the vanishing viscosity results in the literature by weakening the normal and the conormal regularity assumptions, respectively.Citation1Citation2. We require the initial data to be Lipschitz with three integrable conormal derivatives. We also assume that the initial normal derivative has one or two integrable conormal derivatives, depending on the sign of the friction coefficient. Finally, we establish the existence and uniqueness of the Euler equations with a bounded normal derivative, two bounded conormal derivatives, and three integrable conormal derivatives.