Global weak solutions to the Stochastic Ericksen--Leslie equations in dimension two

Hengrong Du; Changyou Wang

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arXiv · 2011.09355

Global weak solutions to the Stochastic Ericksen--Leslie equations in dimension two

Hengrong Du·Changyou Wang

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Abstract

We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen--Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The construction of solutions is based on the convergence of Ginzburg--Landau approximations. To achieve such a convergence, we first utilize the concentration-cancellation method for the Ericksen stress tensor fields based on a Pohozaev type argument, and second the Skorokhod compactness theorem, which is built upon a uniform energy estimate.

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Hengrong Du, Changyou Wang. 2020-11-18. Global weak solutions to the Stochastic Ericksen--Leslie equations in dimension two. https://arxiv.org/abs/2011.09355

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