# Reproductive strong solutions of Navier-Stokes equations with non homogeneous boundary conditions - Mathematics Analysis of PDEs

Abstract: The object of the present paper is to show the existence and the uniquenessof a reproductive strong solution of the Navier-Stokes equations, i.e. thesolution $\boldsymbol{u}$ belongs to $\text{}\mathbf{L}% ^{\infty}0,T;V \cap\mathbf{L}^{2}0,T;\mathbf{H}% ^{2}\Omega$ and satisfies the property$\boldsymbol{u}% \boldsymbol{x,}T =\boldsymbol{u}% \boldsymbol{x,}0=\boldsymbol{u} {0}\boldsymbol{x}$. One considers the case of anincompressible fluid in two dimensions with nonhomogeneous boundary conditions,and external forces are neglected.

Author: Chérif Amrouche LMA - Pau, Macaire Batchi LMA - Pau, Latep, Jean Batina LATEP

Source: https://arxiv.org/