On Asymptotic Behavior of Solutions of a Perturbed Non–Steady Stokes Equation in an Exterior Domain

Abstract:- We formulate sufficient conditions for partial uniform boundedness of the analytic semigroup generated by a perturbed non–steady Stokes operator L in an exterior domain. In spite of the existence of an essential spectrum, we show that the partial (or full) uniform boundedness of the semigroup depends on the behavior of the resolvent operator of L on a finite dimensional space. Key-Words:- The Stokes equation, Analytic semigroups