Navier–Stokes equations with first order boundary conditions

Abstract

On the basis of semigroup and interpolation-extrapolation techniques we derive existence and uniqueness results for the Navier-Stokes equations. In contrast to many other papers devoted to this topic, we do not complement these equations with the classical Dirichlet (no-slip) condition, but instead consider stress-free or slip boundary conditions. We also study various regularity properties of the solutions obtained and provide conditions for global existence