On a $\nu$-continuous family of strong solutions to the Euler or Navier-Stokes equations with the Navier-Type boundary condition

Abstract

Under assumptions on smoothness of the initial velocity and theexternal body force, we prove that there exists T0 > 0, V* > 0and a unique family of strong solutions uv of the Euler or Navier-Stokes initial-boundary value problem on the time interval (0, T0), depending continuously on the viscosity coefficient $\nu$for $0\leq\nu*.The solutions of the Navier-Stokes problem satisfy a Navier-typeboundary condition. We give the information on the rate of convergence of the solutions of the Navier-Stokes problem to the solution of the Euler problem for $\nu\to 0+$.