The well-posedness and the regularity of global attractor for a couple stress fluid through porous layer with the local thermal non-equilibrium effect

TL;DR

This paper establishes the existence, uniqueness, and smoothness of the global attractor for a coupled stress fluid model in porous media with thermal effects, advancing understanding of its long-term behavior.

Contribution

It proves the well-posedness and regularity of the global attractor for the coupled stress fluid model with thermal non-equilibrium effects in porous media.

Findings

Existence and uniqueness of global weak solutions.

Existence of a $C^{ abla}$ smooth global attractor.

The attractor is shown to be $C^{ abla}$-smooth and infinitely differentiable.

Abstract

In the article, we aim to investigate the well-posedness of solution and the regularity of the global attractor for the couple stress fluid in saturated porous media with the local thermal non-equilibrium effect. To be more specific, we firstly show the existence and uniqueness of global weak solution to the model by making use of the standard Galerkin method. Second, relying on verifying the uniformly compact condition required, we prove the existence of the global attractor of the model in the space where the weak solution resides. Finally, we improve the regularity of global attractor by uniformly compact condition and obtain the $C^{\infty}$ attractor for the model.