报告题目: On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids: Existence of Solutions in Some Classes of Large Data
报告人：江飞教授(福州大学)
时间： 2021年11月17日 (周三), 10:00-11:00 (上午)
腾讯会议：612 509 308
邀请人：周建丰
报告摘要: In this talk, we consider the existence of solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in there-dimensional periodic domains (in Lagrangian coordinates). Motivated by the magnetic inhibition mechanism of Lagrangian coordinates version in our previous paper the approximate theory of non-resistive MHD equations and the Diophantine condition imposed by Chen--Zhang--Zhou, we prove the existence and uniqueness of classical solutions under some class of large initial perturbations, where the intensity of impressive magnetic fields depends increasingly on the $H^{17}$-norm of the initial perturbation value of both the velocity and magnetic field. Our result not only mathematically verifies that magnetic fields prevent the formation of singularities of solutions with large initial velocity in the viscous case, but also provide a starting point for the existence theory of large perturbation solutions of non-resistive viscous MHD equations. In addition, we further rigorously prove that, for large time or strong magnetic field, the MHD equations reduce to the corresponding linearized equations by providing the error estimates, which enjoy the types of algebraic decay with respect time or magnetic field, between the solutions of the both nonlinear and linear equations.
报告人简介：江飞教授，硕博连读于厦门大学数学科学学院，曾在北京应用物理与计算数学研究所做两年博士后，2012年9月入职福州大学，并于2017年7月应聘为教授及博士生导师。目前主要研究流体动力学中各类偏微分方程组的适定性问题及解的性态。承担过国家青年项目，福建省面上、自然科学基金杰青及重点项目各一项；曾获得第四届中国工业与应用数学学会“应用数学青年科技奖”，发表论文SCI数学论文40余篇。此外，多次访问香港中文大学数学研究所，复旦大学数学科学学院，北京九所，香港城市大学数学系等单位开展学术合作研究。
