37000gcom威尼斯2024第 22期 数理大讲堂

主讲人： 张挺  教授

主持人： 杜利怀 博士

讲座时间：2024年6月27日下午15：30-16：30

讲座地点：37000gcom威尼斯3B205

讲座题目：Global existence of weak solutions for 3D incompressible inhomogeneous asymmetric fluids

Abstract: In this paper, we study the global existence of weak solutions and the lifespan of strong solutions to 3D inhomogeneous incompressible asymmetric fluids equations. By using the energy method and decomposing technique, the global Fujita–Kato solutions for the asymmetric fluids with initial velocity being sufficiently small in the critical Besov space and with initial density in the bounded function space and have positive lower bounded is obtained. Besides, the estimate of the lifespan of strong solutions to 3D inhomogeneous incompressible asymmetric fluids equations is investigated. This result corresponds to the celebrated Leray estimate on the lifespan of strong solutions to the classical Navier–Stokes equations in Leray (Acta Math, 63:193–248, 1934) and the interesting results for 3Dinhomogeneous incompressibleNavier–Stokes equations in Zhang (Adv Math, 363:107007, 2020). (Joint work with Chenyin Qian, Hui Chen)

个人简介：张挺，理学博士，浙江大学数学科学学院教授，博士生导师，数学科学学院数学系系主任，曾入选国家万人计划“青年拔尖人才支持计划”，教育部“新世纪优秀人才支持计划”,浙江省杰出青年科学基金项目获得者，浙江省“新世纪151人才工程”第二层次培养人员,教育部自然科学奖二等奖，基础学科拔尖学生培养计划2.0，优秀管理人员奖，浙江省教学成果奖一等奖。主要研究Navier-Stokes方程组及其相关流体力学方程组的数学理论。迄今已在《Arch. Rational Mech. Anal.》、《Math. Ann.》、《Commun. Math. Phys.》等国际知名期刊发表SCI文章100多篇