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

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  • Under assumptions on smoothness of the initial velocity and the external body force, we prove that there exists T0 > 0, V* > 0 and 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< $ V*. The solutions of the Navier-Stokes problem satisfy a Navier-type boundary 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 $\nu\to 0+$.
    Mathematics Subject Classification: 35Q30, 35Q31, 76D05, 76D09.

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