Existence and convergence of the Beris-Edwards system with general Landau-de Gennes energy

TL;DR

This paper proves the existence of strong solutions for the Beris-Edwards system with general Landau-de Gennes energy and shows that biaxial solutions converge smoothly to uniaxial solutions over time.

Contribution

It establishes the existence of strong solutions for uniaxial Q-tensors and demonstrates convergence of biaxial solutions to uniaxial solutions under general energy conditions.

Findings

Existence of strong solutions for uniaxial Q-tensors.

Smooth convergence of biaxial to uniaxial solutions.

Applicability to systems with four elastic constants.

Abstract

In this paper, we investigate the Beris-Edwards system for both biaxial and uniaxial $Q$-tensors with a general Landau-de Gennes energy density depending on four non-zero elastic constants. We prove existence of the strong solution of the Beris-Edwards system for uniaxial $Q$-tensors up to a maximal time. Furthermore, we prove that the strong solutions of the Beris-Edwards system for biaxial $Q$-tensors converge smoothly to the solution of the Beris-Edwards system for uniaxial $Q$-tensors up to its maximal existence time.