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

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arxiv 1404.3254 v1 pith:MY3TDZT5 submitted 2014-04-12 math.AP

Wenya Ma , Jinkai Li , Huajun Gong This is my paper · ORCID
classification math.AP
keywords nablaericksen-leslieglobalmathbbsolutionsstrongsystemblow
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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}.

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