报告题目：Some results on compressible non-isentropic MHD equations with partial dissipation

报  告 人：赵雅娟博士（郑州大学）

报告时间：2026年3月31日（周二）15:00--15:45

报告地点：龙洞校区行政楼607

Abstract：In this lecture we discuss the global well-posedness for two classes of compressible non-isentropic magnetohydrodynamic (MHD) equations with partial dissipation. First, to elucidate the physical mechanism whereby the magnetic equation can lack explicit viscosity while the overall system remains dissipative, we study a special 2.5-D viscous non-resistive MHD model. By exploiting the cancellation structure of the system and introducing several new unknown quantities，we give the global well-posedness of strong solutions for this partially dissipative system. In addition, exponential decay of the solutions is obtained. Second, through an analysis of the interaction between inviscid compressible flows and magnetic fields, we establish the existence of global smooth solutions near an appropriately chosen background magnetic field for the inviscid resistive case on two dimensional torus ${\mathbb{T}}^2$. Moreover, we also derive the time decay for the solutions. This result provides rigorous mathematical validation for the experimentally observed stabilization effect of magnetic fields on electrically conductive fluid flows, providing theoretical support for plasma confinement techniques and astrophysical plasma dynamics.

报告人简介：赵雅娟，郑州大学副教授，硕士生导师。2021年于华南理工大学获得应用数学博士学位，主要从事非线性偏微分方程的数学理论研究。近年来，在 Proc. Amer. Math. Soc., J. Math. Fluid Mech., J. Math. Phys., Acta Math. Sci. Ser. B, NoDEA 等国际知名期刊发表多篇论文。主持或获得包括博士后特别资助、国家资助博士后研究人员计划（C档）、河南省青年科学基金在内的多项科研项目。