报告题目：The Cauchy problem for an inviscid Oldroyd-B model in three dimensions: global well posedness and optimal decay rates

报 告 人：刘斯丽（长沙理工大学）

报告时间：2023年10月18日  16:20-17:40

报告地点：格物楼307报告厅

报告摘要：

In this talk I will introduce our recent work on the Cauchy problem for an inviscid compressible Oldroyd-B model in three dimensions. The global well posedness of strong solutions and the associated time-decay estimates in Sobolev spaces are established near an equilibrium state. The vanishing of viscosity is the main challenge compared with [Wang-Wen, Sci. China Math., 2021] where the viscosity coefficients are included and the decay rates for the highest-order derivatives of the solutions seem not optimal. One of the main objectives of this paper is to develop some new dissipative estmates such that the smallness of the initial data and decay rates are independent of the viscosity. Moreover, we prove that the decay rates for the highestorder derivatives of the solutions are optimal, which is of independent interest. Our proof relies on Fourier theory and delicate energy method. This talk is based on joint works with Prof. Wenjun Wang and Prof. Huanyao Wen.

报告人简介：

刘斯丽，长沙理工大学数学与统计学院讲师、硕士研究生导师。博士毕业于华南理工大学，师从温焕尧教授，主要致力于流体力学中的偏微分方程的相关理论研究。目前已在SIAM Journal of Mathematical Analysis等国际知名刊物上发表数篇论文，主持国家自然科学基金青年基金项目1项和湖南省自然科学基金青年基金项目1项。