∈ - varepsilon-regularity criteria and the number of singular points for the 3D simplified Ericksen-Leslie system

Abstract

In this paper, we present a new regularity criteria for suitable weak solutions to the 3D simplified Ericksen-Leslie system. Moreover, under the condition \|\mathbf{u}\|_{L^{q,\infty}_tL^p_x(Q_r(z_0))}+ \|\nabla\mathbf{d}\|_{L^{q,\infty}_tL^p_x(Q_r(z_0))}=K<\infty,~ (\frac{3}{p}+\frac{2}{q}=1~\rm{and}~3