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Global Solutions to the 2D Viscous, Non-resistive MHD System with Large Background Magnetic Field

Prof. Ting Zhang, (Zhejiang University)
15:00-16:00, 17 February 2014  Room 379, Geography Building, Putuo Campus

 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.

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