A Global 2D Well-Posedness Result on the Order Tensor Liquid Crystal\n Theory

2015/11/02 by Francesco De Anna, De Anna, Francesco · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Fibroblast Growth Factor Research #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1511.00582

openalex publication_date 2015/11/02 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Paicu and Zarnescu have studied an order tensor system which describes the\nflow of a liquid crystal. They have proven the existence of weak solutions, the\npropagation of higher regularities, namely H^s with s>1 and the weak-strong\nuniqueness in dimension two. This paper is devoted to the propagation of lower\nregularities, namely H^s for 0<s\≤ 1 and to prove the uniqueness of the\nweak solutions. For the completeness of this research, we also propose an\nalternative approach in order to prove the existence of weak solutions.\n

Cited by

• The global well-posedness for the Q-tensor model of nematic liquid crystals in the half-space
• Weak-strong uniqueness of the full coupled Navier-Stokes and Q-tensor system in dimension three
• Global Regularity to the liquid crystal flows of Q-tensor model

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