主讲人：雷震 教授（复旦大学）

时  间： 3月10日（周四）11：00-12：00

地  点：数学科学学院 310教室

备  注：Abstract: Let $v(x, t)= v^r e_r + v^\theta e_\theta + v^z e_z$ be a solution to the three-dimensional incompressible axially-symmetric Navier-Stokes equations. Denote by $b = v^r e_r + v^z e_z$ the radial-axial vector field. Under a general scaling invariant condition on $b$, we prove that the quantity $\Gamma = r v^\theta$ is H\"older continuous at $r = 0$, $t = 0$. As an application, we give a partial proof of a conjecture on Liouville property by Koch-Nadirashvili-Seregin-Sverak in \cite{KNSS} and Seregin-Sverak in \cite{SS}. As another application, we prove that if $b \in L^\infty([0, T], BMO^{-1})$, then $v$ is regular. This solves an open question raised by Koch and Tataru in \cite{KochTataru} in the axially-symmetric case.