Stability for a 3D Ladyzhenskaya fluid model with unbounded variable delay

Abstract

This paper is concerned with the stability of solutions to a Ladyzhenskaya fluid model with unbounded variable delay. We first prove the existence, uniqueness and regularity of global weak solutions to the Ladyzhenskaya model by using Galerkin approximations and the energy method based on some suitable assumptions about external forces. Then we obtain that the stationary solution is locally stable. Finally, we establish that the stationary solution has polynomial stability in a particular case of unbounded variable delay.

Keywords

• ladyzhenskaya model
• unbounded variable delays
• asymptotic stability