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arXiv · 2011.00100

On strong solution to the 2D stochastic Ericksen-Leslie system: A Ginzburg-Landau approximation approach

Zdzislaw Brzezniak·Gabriel Deugoue·Paul Andre Razafimandimby
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Abstract

In this manuscript, we consider a highly nonlinear and constrained stochastic PDEs modelling the dynamics of 2-dimensional nematic liquid crystals under random perturbation. This system of SPDEs is also known as the stochastic Ericksen-Leslie equations (SELEs). We discuss the existence of local strong solution to the stochastic Ericksen-Leslie equations. In particular, we study the convergence the stochastic Ginzburg-Landau approximation of SELEs, and prove that the SELEs with initial data in $\sh^1\times \sh^2$ has at least a martingale, local solution which is strong in PDEs sense.

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Zdzislaw Brzezniak, Gabriel Deugoue, Paul Andre Razafimandimby. 2020-10-30. On strong solution to the 2D stochastic Ericksen-Leslie system: A Ginzburg-Landau approximation approach. https://arxiv.org/abs/2011.00100

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