Global weak solution for a coupled compressible Navier-Stokes and Q-tensor system

TL;DR

This paper proves the existence and analyzes the long-term behavior of weak solutions for a complex coupled system modeling nematic liquid crystal flow, combining compressible Navier-Stokes equations with Q-tensor dynamics.

Contribution

It establishes the global existence of weak solutions for the coupled compressible Navier-Stokes and Q-tensor system in three dimensions, utilizing weak convergence and compactness methods.

Findings

Existence of global weak solutions is proven.

Long-time dynamics of solutions are characterized.

Key role of Q-tensor symmetry and traceless properties in analysis.

Abstract

In this paper, we study a coupled compressible Navier-Stokes/Q-tensor system modeling the nematic liquid crystal flow in a three-dimensional bounded spatial domain. The existence and long time dynamics of globally defined weak solutions for the coupled system are established, using weak convergence methods, compactness and interpolation arguments. The symmetry and traceless properties of the Q-tensor play key roles in this process.