Regularity and long-time behavior for a thermodynamically consistent model for complex fluids in two space dimensions

TL;DR

This paper establishes enhanced regularity, uniqueness, and long-term behavior of solutions for a thermodynamically consistent two-phase fluid model in two dimensions, including the existence of a global attractor.

Contribution

It provides new regularity results, proves uniqueness, and characterizes the long-time dynamics of the model in a 2D setting, extending previous work.

Findings

Proved additional regularity properties of solutions.

Established uniqueness of solutions.

Characterized the long-time behavior and global attractor.

Abstract

We consider a thermodynamically consistent model for the evolution of thermally conducting two-phase incompressible fluids. Complementing previous results, we prove additional regularity properties of solutions in the case when the evolution takes place in the two-dimensional flat torus with periodic boundary conditions. Thanks to improved regularity, we can also prove uniqueness and characterize the long-time behavior of trajectories showing existence of the global attractor in a suitable phase-space.