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Transactions of the American Mathematical Society

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Global strong solution to the density-dependent incompressible flow of liquid crystals


Authors: Xiaoli Li and Dehua Wang
Journal: Trans. Amer. Math. Soc. 367 (2015), 2301-2338
MSC (2010): Primary 35A05, 76A10, 76D03
DOI: https://doi.org/10.1090/S0002-9947-2014-05924-2
Published electronically: November 12, 2014
MathSciNet review: 3301866
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Abstract: The initial-boundary value problem for the density-dependent incompressible flow of liquid crystals is studied in a three-dimensional bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness are established for both the local strong solution with large initial data and the global strong solution with `small' data. It is also proved that when the strong solution exists, a weak solution with the same data must be equal to the unique strong solution.


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Additional Information

Xiaoli Li
Affiliation: Institute of Applied Physics and Computational Mathematics, Beijing 100088, People’s Republic of China
Address at time of publication: College of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, People’s Republic of China
Email: xlli@bupt.edu.cn

Dehua Wang
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: dwang@math.pitt.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-05924-2
Keywords: Liquid crystals, incompressible flow, density-dependent, global strong solution, existence and uniqueness.
Received by editor(s): January 3, 2012
Received by editor(s) in revised form: June 27, 2012
Published electronically: November 12, 2014
Additional Notes: The first author’s research was supported in part by the National Natural Science Foundation of China under grant 11401036, by the National Natural Science Foundation of China under grants 11271052 and 11471050, by the China Postdoctoral Science Foundation Funded Project under grant 2013T60085, and by the Fundamental Research for the Central Universities No. 2014 RC 0901
The second author’s research was supported in part by the National Science Foundation under grant DMS-0906160, and by the Office of Naval Research under grant N00014-07-1-0668.
Article copyright: © Copyright 2014 American Mathematical Society

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