Local and global solutions on arcs for the Ericksen -- Leslie problem in the whole space
Analysis of PDEs
2023-05-24 v1
Abstract
The work deals with the Ericksen-Leslie System for nematic liquid crystals on the whole space. In our work we suppose the initial condition of the orientation field stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence for small initial data of a solution in low regularity Sobolev spaces.
Keywords
Cite
@article{arxiv.2305.14192,
title = {Local and global solutions on arcs for the Ericksen -- Leslie problem in the whole space},
author = {Daniele Barbera and Vladimir Georgiev},
journal= {arXiv preprint arXiv:2305.14192},
year = {2023}
}
Comments
40 p