Uniform measure attractors for nonautonomous stochastic tamed 3D Navier–Stokes equations with almost periodic forcing

Abstract

This article provides a characterization of uniform measure attractors for non-autonomous stochastic tamed 3D Navier–Stokes equations, specifically with a almost-periodic external force term. The existing literature has primarily focused on measure attractors within an autonomous framework; however, when the forcing function is almost periodic, the solution process generated by the corresponding equations behaves as a non-autonomous Markov process, rendering the existing framework inapplicable. Therefore, it is crucial to investigate this within a new framework, which is the motivation behind the study of uniform measure attractors in this paper.