Global Strong Solutions to Incompressible Ericksen-Leslie System in $\mathbb R^3$

Wenya Ma; Jinkai Li; Huajun Gong

Global Strong Solutions to Incompressible Ericksen-Leslie System in $\mathbb R^3$

Analysis of PDEs 2014-04-15 v1

Authors: Wenya Ma , Jinkai Li , Huajun Gong

Abstract

In this paper, we consider the Cauchy problem to the Ericksen-Leslie system of liquid crystals in $\mathbb R^3$ . Global well-posedness of strong solutions are obtained under the condition that the product of $\|u_0\|_2+\|\nabla d_0\|_2$ and $\|\nabla u_0\|_2+\|\nabla^2d_0\|_2$ is suitably small. This result can be viewed as a supplement to the local existence and blow up criteria discussed in \cite{Hong1}.

Keywords

Ericksen-Leslie system liquid crystals global strong solutions Cauchy problem well-posedness

Cite

@article{arxiv.1404.3254,
  title  = {Global Strong Solutions to Incompressible Ericksen-Leslie System in $\mathbb R^3$},
  author = {Wenya Ma and Jinkai Li and Huajun Gong},
  journal= {arXiv preprint arXiv:1404.3254},
  year   = {2014}
}

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