English

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

Probability 2020-11-03 v1 Analysis of PDEs

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 sh1×sh2\sh^1\times \sh^2 has at least a martingale, local solution which is strong in PDEs sense.

Keywords

Cite

@article{arxiv.2011.00100,
  title  = {On strong solution to the 2D stochastic Ericksen-Leslie system: A Ginzburg-Landau approximation approach},
  author = {Zdzislaw Brzezniak and Gabriel Deugoue and Paul Andre Razafimandimby},
  journal= {arXiv preprint arXiv:2011.00100},
  year   = {2020}
}