Reproductive strong solutions of Navier-Stokes equations with non homogeneous boundary conditions

Abstract

The object of the present paper is to show the existence and the uniqueness of a reproductive strong solution of the Navier-Stokes equations, i.e. the solution $\mathbf{u}$ belongs to $\mathbf{L}$ and satisfies the property $\mathbf{u}$. One considers the case of an incompressible fluid in two dimensions with nonhomogeneous boundary conditions, and external forces are neglected.

18 pages