Energy conservation of the weak solution and the lower bound of possible singular solutions for a simplified three‐dimensional Ericksen–Leslie system

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.