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 u belongs to L% ∞(0,T;V) L2(0,T;H% 2()) and satisfies the property u% (x,T) =u% (x,0) =u0(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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