Zu Chongzhi Mathematics Research Seminar

Date and Time (China standard time): Friday, November 3, 2:00-3:00 pm

Location: WDR 1007

Zoom: 947 1355 7094; Passcode: dkumath

Title: Strong relaxation limits of some partially dissipative systems

Speaker: Ling-Yun Shou

Bio: Ling-Yun Shou obtained his PhD from the Capital Normal University in 2022. He is currently a postdoctor at Nanjing University of Aeronautics and Astronautics. His research interests are large-time behaviors and singular limits of various kinds of PDEs, including compressible Navier-Stokes equations, two-phase flow models, and partially dissipative hyperbolic systems. 

Abstract: 

We study the diffusive relaxation limits of partially dissipative systems in the whole space. The solutions are split into low and high frequencies with a sharp parameter-dependent threshold in suitable hybrid Besov spaces, where the low frequencies are characterized by behaviors of limiting solutions while the high frequencies equipped with critical norms decay as the relaxation parameter vanishes. This approach allows us to establish qualitative and uniform regularity estimates with respect to the time and the parameter. As applications, we investigate three relaxation limit processes:

(1) The hyperbolic-parabolic chemotaxis system for vasculogenesis to a parabolic-elliptic Keller-Segel model;

(2) The one-velocity Baer-Nunziato bi-fluid system to a new two-phase porous media model;

(3) The diffusively scaled Jin-Xin approximation to viscous conservation laws.

This is joint with T. Crin-Barat, Q. He and J. Tan.