Taiwanese Journal of Mathematics

Global Existence and Exponential Decay of Strong Solutions to the 2D Density-dependent Nematic Liquid Crystal Flows with Vacuum

Yang Liu

Advance publication

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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.

Article information

Source
Taiwanese J. Math., Advance publication (2020), 24 pages.

Dates
First available in Project Euclid: 4 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1583290812

Digital Object Identifier
doi:10.11650/tjm/200207

Subjects
Primary: 76A15: Liquid crystals [See also 82D30] 35B65: Smoothness and regularity of solutions 35Q35: PDEs in connection with fluid mechanics

Keywords
incompressible nematic liquid crystal flow strong solutions vacuum exponential decay

Citation

Liu, Yang. Global Existence and Exponential Decay of Strong Solutions to the 2D Density-dependent Nematic Liquid Crystal Flows with Vacuum. Taiwanese J. Math., advance publication, 4 March 2020. doi:10.11650/tjm/200207. https://projecteuclid.org/euclid.twjm/1583290812


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