Uniform Regularity for the Navier–Stokes Equation with Navier Boundary Condition

By Nader Masmoudi, Frédéric Rousset. Archive for Rational Mechanics and Analysis, 2010

189 citations recorded by the source corpus.

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier–Stokes equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in L∞. This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d67af95ae52015f47665f581637c8a9728446252

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Citations in the corpus

Vanishing Viscous Limits for 3D Navier–Stokes Equations with a Navier-Slip Boundary Condition (2012, background): “More recently, Masmoudi and Rousset [21] proved that the solutions to (1.1) converge uniformly to the one of the Euler equations in the spatial and time variables under the frame of conormal Sobolev space.”
Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier–Stokes Equations (2012, methodology): “As in our previous work [40], it is convenient for this estimate to use a coordinate system where the Laplacian has the simplest expression.”
Local‐in‐Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods (2012, background): “Let us also mention that when considered in the whole space [28, 12, 19] or with other boundary conditions such as Navier boundary condition [32, 11, 2, 20] or incoming flow [30], the convergence problem becomes simpler since there is no boundary layer or the boundary layer is stable.”
The Inviscid Limit of Navier–Stokes Equations for Analytic Data on the Half-Space (2017, background): “2); see, for instance, [21, 28, 9], and also the review papers [3, 27].”