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October, 2020 Global Existence and Exponential Decay of Strong Solutions to the 2D Density-dependent Nematic Liquid Crystal Flows with Vacuum
Yang Liu
Taiwanese J. Math. 24(5): 1205-1228 (October, 2020). DOI: 10.11650/tjm/200207

Abstract

This paper deals with the 2D incompressible nematic liquid crystal flows with density-dependent viscosity in bounded domain. The global well-posedness of strong solutions are established in the vacuum cases, provided the assumption that $\overline{\rho} + \|\nabla d_0\|_{L^2}$ is suitably small with large velocity, which extends the recent work [Discrete Contin. Dyn. Syst. 37 (2017), 4907--4922] and [Methods Appl. Anal. 22 (2015), 201--220] to the case of variable viscosity. Furthermore, the exponential decay of the solution is also obtained.

Citation

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Yang Liu. "Global Existence and Exponential Decay of Strong Solutions to the 2D Density-dependent Nematic Liquid Crystal Flows with Vacuum." Taiwanese J. Math. 24 (5) 1205 - 1228, October, 2020. https://doi.org/10.11650/tjm/200207

Information

Received: 8 September 2019; Revised: 10 January 2020; Accepted: 25 February 2020; Published: October, 2020
First available in Project Euclid: 4 March 2020

MathSciNet: MR4152663
Digital Object Identifier: 10.11650/tjm/200207

Subjects:
Primary: 35B65, 35Q35, 76A15

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 5 • October, 2020
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