2019年新葡新京平台学术报告(四十二)

题目Regularity of trajectory attractor and trajectory statistical solution forthe 3D globally modified Navier-Stokes equations

报告专家赵才地温州大学数理学院教授、温州大学应用数学研究所所长、硕士生导师

报告时间: 20191120日(周三)下午14:30-16:00

报告地点: 东校区8406

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摘要We first prove the existence and regularity of the trajectoryattractor for a three-dimensional system of globally modified Navier-Stokesequations. Then we use the natural translation semigroup and trajectory attractorto construct the trajectory statistical solutions in the trajectory space.In our construction thetrajectory statistical solution is an invariant Borel probability measure,which is supported by the trajectory attractor and is invariant under

the action of the translation semigroup. As a byproduct of the regularity of thetrajectory attractor, we obtain the asymptotic regularity of the trajectory statisticalsolution in the sense that it is supported by a setin the trajectory space in which all weak solutions are in factstrong solutions.

 

个人简介赵才地博士,温州大学数理学院教授,硕士生导师,美国数学会《数学评论》和德国《数学文摘》评论员,韩国全南大学应用数学专业兼职博导,目前任温州大学应用数学研究所所长,温州大学学术委员会。 2008 年入选浙江省高校优秀青年教师资助计划,2012 入选温州市“新世纪 551 人才工程”第一层次和浙江省“新世纪151人才”第二层次。主持国家级自然科学基金4项,浙江省自然科学基金2项,中国博士后科学基金1项,曾获浙江省自然科学优秀论文二等奖、浙江省自然科学三等奖、浙江省高校优秀科研成果奖。在《J Differential Equations》,《Nonlinearity》,《J. Math. Fluids Mech.J Evolution Equations》,《 Quarterly Appl. Math.Discrete Cont. Dyn. Syst.,J. Math. Phys.《中国科学》、《数学学报》等国内外主流数学期刊上发表专业文论文 60 余篇其中 SCI收录50余篇。