报告时间：2022/12/09 开始时间：下午3:00

报告地址：腾讯会议：858-149-564

报告题目：Global existence of weak solutions for 3D incompressible inhomogeneous asymmetric fluids

摘要： 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)

报告人简介： 张挺，理学博士，浙江大学数学科学学院教授，博士生导师，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。主要研究方向是偏微分方程及其应用。考虑了有重要物理背景的一类粘性依赖于密度的Navier-Stokes方程的自由边界问题。当密度为零时，粘性系数会退化为零，使问题产生了本质的困难。考虑不同情况，如密度是否连续、有无外力影响、有无外压强影响等，研究了一维系统或球面对称系统的整体（局部）适定性、解的渐近性态和收敛率估计等问题。利用调和分析方法，在各向异性的Sobolev-Besov空间中，研究了粘性是各向异性的三维Navier-Stokes方程组的整体（局部）适定性问题。利用概率论方法，探讨不可压缩 Navier-Stokes方程组在低正则性空间中的适定性问题等。在《Arch. Rational Mech. Anal.》、《Commun. Math. Phys.》等杂志上发表文章九十多篇。