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

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

2007-04-18

arxiv.org/abs/0704.2360v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

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 $\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 an incompressible fluid in two dimensions with nonhomogeneous boundary conditions, and external forces are neglected.

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