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Global well‐posedness of the nonhomogeneous incompressible liquid crystals systems
Author(s) -
Niu Dongjuan,
Xi Xiaoyu
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3886
Subject(s) - bounded function , compressibility , liquid crystal , mathematics , domain (mathematical analysis) , initial value problem , space (punctuation) , mathematical analysis , value (mathematics) , mechanics , physics , condensed matter physics , computer science , operating system , statistics
This paper examines the initial‐value problem for the nonhomogeneous incompressible nematic liquid crystals system with vacuum. This paper establishes two main results. The first result is involved with the global strong solutions to the 2D liquid crystals system in a bounded smooth domain. Our second result is concerned with the small data global existence result about the 3D system in the whole space. In addition, the local existence and a blow‐up criterion of strong solutions are also mentioned. Copyright © 2016 John Wiley & Sons, Ltd.