Global Solvability of the Inhomogeneous Ericksen-Leslie System with only\n Bounded Density

2015/03/05 by Francesco De Anna, De Anna, Francesco
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1503.01623

openalex publication_date 2015/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ericksen and Leslie established a theory to model the flow of nematic liquid\ncrystals. This paper is devoted to the Cauchy Problem of a simplified version\nof their system, which retains most of the properties of the original one. We\nconsider the density-dependent case and we establish the global existence of\nsolutions in the whole space for small initial data. The initial density only\nhas to be bounded and kept far from vacuum, while the initial velocity belongs\nto some critical Besov Space. Under a little bit more regularity for the\ninitial velocity, we prove also that those solutions are unique.\n

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