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Volume 2, Issue 3
Global Solutions of Nematic Liquid Crystal Flow in Dimension Two

Yuan Chen & Yong Yu

DOI: 10.4208/cmaa.2023-0004

Commun. Math. Anal. Appl., 2 (2023), pp. 304-356.

Published online: 2023-09

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  • Abstract

In this article we are concerned with a simplified Ericksen-Leslie system on $\mathbb{R}^2,$ whose bounded domain case was considered in [Lin et al., Arch. Ration. Mech. Anal. 197 (2010), 297–336]. With a study of its vorticity-stream formulation, we establish a global existence result of weak solutions when initial orientation has finite energy and initial vorticity function lies in $L^1 (\mathbb{R}^2).$

  • Keywords

Ericksen-Leslie system, circulation Reynolds number, vorticity formulation.

  • AMS Subject Headings

35A01, 35D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-2-304, author = {Chen , Yuan and Yu , Yong}, title = {Global Solutions of Nematic Liquid Crystal Flow in Dimension Two}, journal = {Communications in Mathematical Analysis and Applications}, year = {2023}, volume = {2}, number = {3}, pages = {304--356}, abstract = {

In this article we are concerned with a simplified Ericksen-Leslie system on $\mathbb{R}^2,$ whose bounded domain case was considered in [Lin et al., Arch. Ration. Mech. Anal. 197 (2010), 297–336]. With a study of its vorticity-stream formulation, we establish a global existence result of weak solutions when initial orientation has finite energy and initial vorticity function lies in $L^1 (\mathbb{R}^2).$

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2023-0004}, url = {http://global-sci.org/intro/article_detail/cmaa/22016.html} }
TY - JOUR T1 - Global Solutions of Nematic Liquid Crystal Flow in Dimension Two AU - Chen , Yuan AU - Yu , Yong JO - Communications in Mathematical Analysis and Applications VL - 3 SP - 304 EP - 356 PY - 2023 DA - 2023/09 SN - 2 DO - http://doi.org/10.4208/cmaa.2023-0004 UR - https://global-sci.org/intro/article_detail/cmaa/22016.html KW - Ericksen-Leslie system, circulation Reynolds number, vorticity formulation. AB -

In this article we are concerned with a simplified Ericksen-Leslie system on $\mathbb{R}^2,$ whose bounded domain case was considered in [Lin et al., Arch. Ration. Mech. Anal. 197 (2010), 297–336]. With a study of its vorticity-stream formulation, we establish a global existence result of weak solutions when initial orientation has finite energy and initial vorticity function lies in $L^1 (\mathbb{R}^2).$

Yuan Chen & Yong Yu. (2023). Global Solutions of Nematic Liquid Crystal Flow in Dimension Two. Communications in Mathematical Analysis and Applications. 2 (3). 304-356. doi:10.4208/cmaa.2023-0004
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