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Weighted Stepanov-like pseudo almost automorphic solutions for evolution equations and applications. (English) Zbl 1462.35027

Summary: In this paper, the existence and stability of (weighted) Stepanov-like pseudo almost automorphic solutions are proved for a large class of linear and semilinear evolution equations in interpolation spaces. Our method is based on the one hand on a combination of differential inequalities and interpolations functors for the case of linearized equation, and on the other hand on the fixed point argument for the semi-linear equations to handle the case of (weighted) Stepanov-like pseudo almost automorphic functions. Finally, we apply the abstract results to various problems of incompressible viscous fluid flows.

MSC:

35B15 Almost and pseudo-almost periodic solutions to PDEs
35B35 Stability in context of PDEs
35Q30 Navier-Stokes equations
47D06 One-parameter semigroups and linear evolution equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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