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Global Strong Solutions to Incompressible Ericksen-Leslie System in $\mathbb R^3$ (1404.3254v1)
Published 12 Apr 2014 in math.AP
Abstract: In this paper, we consider the Cauchy problem to the Ericksen-Leslie system of liquid crystals in $\mathbb R3$. Global well-posedness of strong solutions are obtained under the condition that the product of $|u_0|_2+|\nabla d_0|_2$ and $|\nabla u_0|_2+|\nabla2d_0|_2$ 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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