题目：Number of singular points and energy equality for the co-rotational Beris-Edwards system modeling
nematic liquid crystal flow
报告人： 刘桥副教授，湖南师范大学
时间地点：2020年12月7日（周一） 上午9：30-10：30， 必赢76net线路唯一官方网站425
摘要： In this talk, we consider the singular points of suitable weak solutions to the 3D co-rotational
Beris-Edwards system modeling thehydrodynamical motion of nematic liquid crystal flows, which is a
coupled system with the Navier-Stokes equations for the fluid and a parabolic system of Q-tensor
for the liquid average orientation. We prove that if (u,Q) defined on $\mathbb{R}^{3}\times (0,T)$
is a suitable weak solution to the 3D co-rotational Beris-Edwards system, and satisfies
\begin{align*}
\|(\u,\nabla Q)\|_{L^{q,\infty}(0,T;L^{p}(\mathbb{R}^{3}))}
<\infty \text{ with }3<p<\infty \text{ and } \frac{2}{q}+\frac{3}{p}=1,
\end{align*}
where $M$ is a positive constant, then for a given open subset $\Omega\subseteq \mathbb{R}^{3}$ and
for a given moment of time $t\in (0,T)$, the number of points of the set $\Sigma(t)\cap \Omega$ is
finite, where $\Sigma(t)\equiv \{(x,t)\in \Sigma\}$ and $\Sigma$ is the set of singular points for
$(u,Q)$. Moreover, if $T_{1}\in(0,T)$ is the first time for singularity appears, we show that the
energy equality holds on the closed interval $[0,T_{1}]$ including the time $T_{1}$.
报告人简介：刘桥，副教授，于2012年获中山大学博士学位。主要研究领域为不可压流体中偏微分方程如Navier--Stokes 方程组和
液晶流系统等的相关数学研究。现主持国家自然科学基金面上项目1项。
