Well-posedness of a fully-coupled Navier-Stokes/Q-tensor system with inhomogeneous boundary data

2013/11/14 by Helmut Abels, Abels, Helmut, Georg Dolzmann +3 · 2 citations
Engineering · Mathematics · #35Q30 #35Q35 #76D03 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1311.3443

openalex publication_date 2013/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove short-time well-posedness and existence of global weak solutions of the Beris--Edwards model for nematic liquid crystals in the case of a bounded domain with inhomogeneous mixed Dirichlet and Neumann boundary conditions. The system consists of the Navier-Stokes equations coupled with an evolution equation for the Q-tensor. The solutions possess higher regularity in time of order one compared to the class of weak solutions with finite energy. This regularity is enough to obtain Lipschitz continuity of the non-linear terms in the corresponding function spaces. Therefore the well-posedness is shown with the aid of the contraction mapping principle using that the linearized system is an isomorphism between the associated function spaces.

Cited by

• The global well-posedness for the Q-tensor model of nematic liquid crystals in the half-space
• L^p-based Sobolev theory for PDEs on closed manifolds of class C^m

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