On the regularity of very weak solutions for an elliptic coupled system\n of liquid crystal flows

2021/04/12 by Oscar Jarrín, Jarrin, Oscar
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2104.05648

openalex publication_date 2021/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider here an elliptic coupled system describing the dynamics of liquid\ncrystals flows. This system is posed on the whole n-dimensional space. We\nintroduce first the notion of very weak solutions for this system. Then, within\nthe fairly general framework of the Morrey spaces, we derive some sufficient\nconditions on the very weak solutions which improve their regularity. As a\nbi-product, we also prove a new regularity criterium for the time-independing\nNavier-Stokes equations.\n

Citations

• Some constitutive equations for liquid crystals
• <i>The Physics of Liquid Crystals</i>

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