Rigorous biaxial limit of a molecular-theory-based two-tensor hydrodynamics

2022/06/21 by Li, Sirui, Xu, Jie · 1 citation
#35A01 #35C20 #35Q35 #76A15 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Soft Condensed Matter (cond-mat.soft)

paper · doi:10.48550/arxiv.2206.10154

Abstract

We consider a two-tensor hydrodynamics derived from the molecular model, where high-order tensors are determined by closure approximation through the maximum entropy state or the quasi-entropy. We prove the existence and uniqueness of local in time smooth solutions to the two-tensor system. Then, we rigorously justify the connection between the molecular-theory-based two-tensor hydrodynamics and the biaxial frame hydrodynamics. More specifically, in the framework of Hilbert expansion, we show the convergence of the solution to the two-tensor hydrodynamics to the solution to the frame hydrodynamics.

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