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Well-posedness of frame hydrodynamics for biaxial nematic liquid crystals

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arxiv 2202.08998 v2 pith:3NMDXYCY submitted 2022-02-18 math.AP

Sirui Li , Chenchen Wang , Jie Xu This is my paper · ORCID
classification math.AP
keywords framebiaxialhydrodynamicsmodelnematicsolutionswell-posednessblow-up
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abstract

We consider the hydrodynamics for the biaxial nematic phase characterized by a field of orthonormal frame, which can be derived from a molecular-theory-based tensor model. In dimension two and three, we establish the local well-posedness and the blow-up criterion for smooth solutions to the frame hydrodynamic model. Furthermore, we prove the global existence of weak solutions in $\mathbb{R}^2$ which are nonsmooth at finitely many singular times.

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