Finite-time attractivity of strong solutions for generalized nonlinear abstract Rayleigh–Stokes equations

Abstract

In the present paper, we address the global solvability and finite-time attractivity of strong solutions for an abstract Rayleigh–Stokes-type equation involving nonlinear perturbations in Hilbert spaces. Based on regularity estimates of resolvent operator, local estimates on Hilbert scales and fixed point arguments, we obtain some results on global existence and finite-time attractivity of strong solutions to our problem.