ORIGINAL PAPER
Energy conservation of the weak solution and the lower bound of possible singular solutions for a simplified three-dimensional Ericksen–Leslie system
Zhongbao Zuo,
Corresponding Author
Zhongbao Zuo
School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
Correspondence
Zhongbao Zuo, School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China.
Email: [email protected]
Search for more papers by this authorZhongbao Zuo,
Corresponding Author
Zhongbao Zuo
School of Mathematics and Statistics, Central South University, Changsha, Hunan, China
Correspondence
Zhongbao Zuo, School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China.
Email: [email protected]
Search for more papers by this authorFirst published: 21 April 2025
Abstract
In this paper, we study the energy balance problem of the weak solutions for a simplified Ericksen–Leslie system. Inspired by the work of Nguyen, Nguyen, and Tang (Nonlinearity, 32: 4206–4231, 2019), based on some delicate commutator estimates and the following additional regularity condition:
we prove the energy equality for the simplified Ericksen–Leslie system in three dimensional periodic domain. Moreover, we give the lower bounds of the possible singular solutions for the simplified Ericksen–Leslie system.
Open Research
DATA AVAILABILITY STATEMENT
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
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