Liquid Crystal Equations with Infinite Energy Local Wellposedness and Blow Up Criterion
Abstract
In this paper, we consider the Cauchy problem of the incompressible liquid crystal equations in $n$ dimensions. We prove the local wellposedness of mild solutions to the liquid crystal equations with $L^\infty$ initial data, in particular, the initial energy may be infinite. We prove that the solutions are smooth with respect to the space variables away from the initial time. Based on this regularity estimate, we employ the blow up argument and Liouville type theorems to establish vorticity direction type blow up criterions for the type I mild solutions established in the present paper.
 Publication:

arXiv eprints
 Pub Date:
 August 2013
 DOI:
 10.48550/arXiv.1309.0072
 arXiv:
 arXiv:1309.0072
 Bibcode:
 2013arXiv1309.0072L
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics