2025数学物理与分析
学术报告
报告题目：Sigma compact pullback attractor and statistical solutions for the semi-dissipative Boussinesq system
报 告 人：赵才地 教授
报告时间：2025年12月09日（周二） 09:00-10:00
腾讯会议：5318371238
报告摘要：In this talk, we discuss the pullback dynamics and statistical solutions for the Boussinesq system involving a dissipative parabolic equation for the velocity field and a conservative hyperbolic equation for the temperature. We adopt the strong topology in space H^1 for the velocity field and employ the weak topology in space L^2 for the temperature, and then prove that the generated evolution process of the solution mappings possesses a sigma compact pullback attractor in space H^1 \times L^2 under this mixed topology. Afterwards, we establish that the evolution process possesses a family of invariant Borel probability measures with supports contained in the obtained pullback attractor. Finally, we prove that a family of probability measures satisfies Liouville's equation and is a statistical solution for the addressed Boussinesq system.
报告人简介：赵才地，温州大学特聘教授，韩国全南大学兼职博导，浙江省新世纪人才，温州市领军人才，主要从事非线性发展方程——无穷维动力系统方面的研究，在《Math. Ann》、《J. Differential Equations》、《Nonlinearity》、《Science China： Math》等期刊上发表论文60余篇，主持国家级科研项目5项（其中自然科学基金面上项目3项），浙江省自然科学基金重点项目1项和面上项目2项，中国博士后科学基金1项，曾获浙江省自然科学三等奖和浙江省数学会优秀科研成果二等奖。