NYU – ECNU
Institute of Mathematical Sciences at NYU Shanghai

WORKING AND LITERATURE SEMINAR

ABSTRACT OF THE TALK

In this paper, we consider the global existence and uniqueness of the solutions to the 2D viscous, non-resistive MHD system. For any initial data, if the background magnetic field is sufficiently large, then we can obtain the global strong solutions.
$\left\{ \begin{align}
& {{\partial }_{t}}b+v\cdot \nabla b=b\cdot \nabla v,\ \ \ \left( t,x \right)\in {{\mathbb{R}}^{+}}\times {{\mathbb{R}}^{2}}, \\
& {{\partial }_{t}}v+v\cdot \nabla v-\Delta v+\nabla p=b\cdot \nabla b, \\
& \text{div}v=\text{div}b=0, \\
& b\left| _{t=0}={{b}_{0}},\ \ v\left| _{t=0}={{v}_{0}}, \right. \right. \\
\end{align} \right.$
$v\left( t,x \right)\to 0,b\left( t,x \right)\to {{\left( \frac{1}{\varepsilon },0 \right)}^{\text{T}}},\text{when}\left| x \right|\to \infty ,$
BIOGRAPHY

Ting Zhang is Professor of Mathematics at Zhejiang University in Hangzhou.