勷勤数学•专家报告

题      目：Global well-posedness and large-time behavior for a special  2.5-D full compressible viscous non-resistive MHD system

报  告  人：翟小平 副教授  (邀请人：叶伟奎)

                                             广东工业大学

时      间：5月9日  15：00-16：00

地     点：数科院西楼114教室

报告人简介:

          翟小平，广东工业大学数学与统计学院副教授。主要从事流体力学偏微分方程组的研究，在相关方向发表Sci论文多篇，主持国家自然科学基金青年基金，广东省自然科学基金青年提升项目和面上项目。曾入选深圳市后备人才计划。

摘      要：

         Physical experiments and numerical simulations have observed a remarkable phenomenon that the energy is dissipated at a rate that is independent of the ohmic resistivity in the magnetohydrodynamic systems. In other words, the viscosity for the magnetic field equation can be zero and the system may still be dissipative. To understand the mechanism of this phenomenon, we will focus on a special $2\frac12$-D compressible MHD flow where the magnetic field is vertical  and examine the stability near a background magnetic field.Due to the lack of dissipation for  density and magnetic field, this stability problem is not trivial. By exploiting the  cancellation structure of the system and introducing several new unknown quantities, we  prove the global well-posedness of strong solutions  in the framework of  Soboles spaces and Besov spaces, respectively. In addition, we also  obtain the exponential decay for this partially dissipative system.

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