報告題目：     Pullback attractors for 2D MHD equations on time-varying domains

報告人:           宋小亞講師

報告人單位：  伟德国际1946官网

報告日期：     2023年11月9日 星期四

報告時間：     15:00-16:00

報告地點：     勵學樓B219 

報告人簡介:  宋小亞，伟德国际1946官网講師，主要研究方向是非線性泛函分析與無窮維動力系統。2019年博士畢業于蘭州大學，師從孫春友教授。2019年7月-2021年11月于廣州大學做博士後，合作導師是曹道民教授。主要研究結果發表在Discrete Contin. Dyn. Syst.，J. Math. Phys.，J. Math. Anal. Appl.，Nonlinear Anal. Real World Appl.等期刊上。主持國家自然科學基金-青年科學項目，中國博士後科學基金面上項目，伟德国际1946官网中央高校基本科研業務費項目等課題。

報告摘要: In the present paper, we consider the asymptotic dynamics of 2D MHD equations  defined on the time-varying domains with homogeneous Dirichlet boundary conditions. First we introduce some coordinate transformations to construct the invariance of the divergence operators in any n-dimensional spaces and establish some equivalent estimates of the vectors between the time-varying domains and the cylindrical domains. Then, we apply these estimates  to overcome the difficulties caused by the variations of the spatial domains, including the processing of the pressure p and the definition of weak solutions. Detailed arguments of converting the equations on the time-varying domains into the corresponding equations on the cylindrical domains are presented. Finally, we show the well-posedness of weak solutions and the existence of a compact pullback attractor for the 2D MHD equations。