Journal article
REMARKS OF GLOBAL WELLPOSEDNESS OF LIQUID CRYSTAL FLOWS AND HEAT FLOWS OF HARMONIC MAPS IN TWO DIMENSIONS
Proceedings of the American Mathematical Society, Vol.142(11), pp.3801-3810
11/01/2014
DOI: 10.1090/S0002-9939-2014-12057-0
Abstract
We consider the Cauchy problem to the two-dimensional incompressible liquid crystal equation and the heat flows of the harmonic maps equation. Under a natural geometric angle condition, we give a new proof of the global wellposedness of smooth solutions for a class of large initial data in energy space. This result was originally obtained by Ding-Lin and Lin-Lin-Wang. Our main technical tool is a rigidity theorem which gives the coercivity of the harmonic energy under a certain angle condition. Our proof is based on a frequency localization argument combined with the concentration-compactness approach which can be of independent interest.
Details
- Title: Subtitle
- REMARKS OF GLOBAL WELLPOSEDNESS OF LIQUID CRYSTAL FLOWS AND HEAT FLOWS OF HARMONIC MAPS IN TWO DIMENSIONS
- Creators
- Zhen Lei - Fudan UniversityDong Li - University of British ColumbiaXiaoyi Zhang - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.142(11), pp.3801-3810
- DOI
- 10.1090/S0002-9939-2014-12057-0
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Number of pages
- 10
- Grant note
- 11171072; 11121101; 11222107 / NSFC 12ZZ012 / Innovation Program of Shanghai Municipal Education Commission Shanghai Talent Development Fund Alfred Sloan Fellowship 09DZ2272900 2 / SGST 0908032; DMS-1128155 / NSF
- Language
- English
- Date published
- 11/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984241039002771
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