学术报告

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

报告时间：2022年4月22日10：00—11:00

报告地点：腾讯会议586 251 919

报告简介：This paper is concerned with the asymptotic behaviors of global strong solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in two-dimensional periodic domains in Lagrangian coordinates. First, motivated by the odevity conditions imposed in [Pan-Zhou-Zhu, Arch. Ration. Mech. Anal. 227 (2018), 637--662], we prove the existence and uniqueness of strong solutions under some class of large initial perturbations, where the strength of impressive magnetic fields depends increasingly on the $H^2$-norm of the initial perturbation value of both the velocity and magnetic field. Then, we establish time-decay rates of strong solutions. Moreover, we find that $H^2$-norm of the velocity decays faster than the perturbed magnetic field. Finally, by developing some new analysis techniques, we show that the strong solution {converges} in a rate of the field strength to a solution of the corresponding linearized problem as the strength of the impressive magnetic field goes to infinity. In addition, an extension of similar results to the corresponding inviscid case with damping is presented.

报告人简介：江飞，福州大学星际电子在线教授，博士生导师，国家优秀青年科学基金获得者。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、面上及优青项目各一项，福建省面上、高校杰青、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”，已在《Adv. Math.》、《Arch. Rational Mech. Anal.》、《J. Math. Pures Appl.》、《Comm. Partial Differential Equations》、《Calc. Var. Partial Differential Equations》等杂志上发表数学论文40余篇。