报告题目：Global existence and stability of solutions for the 2D non-resistive compressible MHD system

报 告 人：朱异

报告时间：2026年6月24日下午15:00 -16:00

腾讯会议：561-888-500

报告摘要：This paper investigates the non-resistive compressible magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. We establish the global existence and stability of classical solutions for initial data sufficiently close to a constant equilibrium state. A distinguishing feature of our result is that global stability is derived solely from pure $H^s$ energy estimates and an intrinsic $L^2$ time-decay mechanism, thereby bypassing the traditional requirement for the initial data of $L^1$ integrability or negative-order Sobolev norm regularity. To achieve this goal, we first introduce a specific quantity motivated by the effective viscous flux, which intrinsically couples the density and magnetic field perturbations. Secondly, to overcome the critical time-decay obstacle arising from the absence of negative-order regularity, we develop a novel pseudo-negative-derivative technique. Moreover, we regard the wildest nonlinear term as a whole and bypass the need to obtain time-decay estimate for individual components. These approaches enable us to close the higher-order energy estimate entirely within standard Sobolev spaces.

个人简介：朱异，华东理工大学数学学院副教授。2017年博士毕业于复旦大学，曾访问美国佐治亚理工学院。主要从事偏微分方程的适定性理论方面的研究，特别是流体力学方程组如磁流体力学方程组、粘弹性力学方程组等。入选上海市“启明星”计划、上海东方英才青年项目。主持国家自然科学基金面上项目。研究成果发表在Adv. Math.、 ARMA、JFA、SIAM J. Math. Anal.、JDE、CVPDE等国际期刊。

初审｜艾成飞

复审｜鲁学伟

终审｜杨汉春