On convergence criteria for incompressible Navier-Stokes equations with Navier boundary conditions and physical slip rates

Yasunori Maekawa (1) , Matthew Paddick (2)

1 Department of Mathematics, Graduate School of Science
2 LJLL - Laboratoire Jacques-Louis Lions

We prove some criteria for the convergence of weak solutions of the 2D incompressible Navier-Stokes equations with Navier slip boundary conditions to a strong solution of incompressible Euler. The slip rate depends on a power of the Reynolds number, and it is increasingly apparent that the power 1 may be critical for L^2 convergence, as hinted at in [hal-01093331].

Mots clés: Navier-Stokes and Euler equations; Inviscid limit; Boundary layer theory; Navier boundary condition

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Yasunori Maekawa, Matthew Paddick. On convergence criteria for incompressible Navier-Stokes equations with Navier boundary conditions and physical slip rates. Mathematical Analysis in Fluid and Gas Dynamics, Jul 2016, Kyôto, Japan. pp.9-23. ⟨hal-01446454⟩