Commun. Math. Anal. Appl., 2 (2023), pp. 304-356.
Published online: 2023-09
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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} }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 $L^1 (\mathbb{R}^2).$