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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Global strong solution to the density-dependent incompressible flow of liquid crystals
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by Xiaoli Li and Dehua Wang PDF
Trans. Amer. Math. Soc. 367 (2015), 2301-2338 Request permission

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
  • 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.
  • © Copyright 2014 American Mathematical Society
  • 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
  • MathSciNet review: 3301866