On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition

Abstract

Provided the initial velocity and the external body force are sufficiently smooth, there exist T 0 > 0 , ν ∗ > 0 and a unique continuous family of strong solutions u ν ( 0 ⩽ ν < ν ∗ ) of the Euler or Navier–Stokes initial–boundary value problem on the time interval ( 0 , T 0 ) . The solutions of the Navier–Stokes problem satisfy a Navier-type boundary condition. To cite this article: H. Bellout et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).