关于举行美国Auburn大学徐欢博士学术报告会的通知

报告题目：Maximal L^1-Regularity for a Class of Parabolic Systems and Applications to Navier-Stokes Equations

报  告  人：徐欢博士（美国Auburn大学）

报告时间：2021年6月25日（星期五）上午9:00~10:00         

报告地点：腾讯会议：503 280 586

邀 请 人：李用声教授

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数学学院

2021年6月23日

报告摘要：We revisit a method initiated by Danchin and Mucha for solving hyperbolic-parabolic systems. The key idea in the Danchin-Mucha framework is to rewrite the hyperbolic-parabolic system by introducing Lagrangian coordinates and investigate the maximal L¹-regularity for the linearized system of the Lagrangian formulation in critical spaces. However, the previous framework only works when the linearized system has constant coefficients. We extend it to adapt to linear systems with variable coefficients by overcoming many difficulties. As applications, we prove the global existence and stability of solutions to incompressible and compressible Navier-Stokes equations with large density oscillations. Our results differ from the existing work in that we discover that the gradient of the velocity has a small L¹L^∞ norm when only the initial velocity is small in critical spaces. This method might be used to solve some other problems arising from fluid dynamics.

报告人简介：徐欢，美国奥本大学博士，研究兴趣主要集中于调和分析在椭圆抛物问题与流体力学方程组中的应用。在国际知名期刊如J. Differential Equations，J. Math. Fluid Mech.，DCDS-A 等上面发表SCI论文多篇。