On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids: Existence of Solutions in Some Classes of Large Data
数学专题报告
报告题目(Title)：On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids: Existence of Solutions in Some Classes of Large Data
报告人(Speaker)：江飞 教授（福州大学数学科学学院）
地点(Place)：腾讯会议号：420346179；密码：1202
时间(Time)：2021年12月2日（周四）下午2:40—3:40.
邀请人(Inviter)：许孝精
报告摘要
This paper is concerned with 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.
