Global well-posedness for Ericksen-Leslie system with zero viscosity

Zhou, Jianfeng

doi:10.1090/proc/16731

Global well-posedness for Ericksen-Leslie system with zero viscosity
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by Jianfeng Zhou;

Proc. Amer. Math. Soc. 152 (2024), 2185-2197

DOI: https://doi.org/10.1090/proc/16731

Published electronically: March 7, 2024

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Abstract:

We study the global well-posedness of the simplified Ericksen-Leslie system with zero viscosity on the periodic domain $\mathbb {T}^2$. Precisely, we prove the global existence and uniqueness of smooth solution to Ericksen-Leslie system if the initial data $(u_0,\nabla d_0)$ is small in $H^4(\mathbb {T}^2)\times H^4(\mathbb {T}^2)$. Furthermore, we derive the time decay estimate of $\nabla d$ in $H^1(\mathbb {T}^2)$.

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