Suitable weak solutions for the co-rotational Beris-Edwards system in dimension three

Abstract

In this paper, we establish the global existence of a suitable weak solution to the co-rotational Beris-Edwards $Q$-tensor system modeling the hydrodynamic motion of nematic liquid crystals with either Landau-De Gennes bulk potential in ${\mathbb{R}}^3$ or Ball-Majumdar bulk potential in ${\mathbb{T}}^3$, a system coupling the forced incompressible Navier-Stokes equation with a dissipative, parabolic system of Q-tensor $Q$ in ${\mathbb{R}}^3$, which is shown to be smooth away from a closed set $\Sigma$ whose $1$-dimensional parabolic Hausdorff measure is zero.

51 pages

Cited by in corpus (1)

• Partial regularity for Navier-Stokes and liquid crystals inequalities without maximum principle