A survey on partially dissipative systems: global well-posedness and strong relaxation limit in the critical regularity setting
Next Monday November 20, 2023 our postdoctoral researcher Dr. Timothée Crin-Barat will talk on “A survey on partially dissipative systems: global well-posedness and strong relaxation limit in the critical regularity setting” at the Nanjing University of Aeronautics and Astronautics, China.
Abstract. In this talk, we review recent results on so-called partially dissipative hyperbolic systems. Such systems model physical phenomena with degenerate dissipative or diffusive terms and appear in many evolution equations. For example, in gas dynamics where the mass is conserved during the evolution, but the momentum balance includes a diffusion (viscosity) or damping (relaxation) term.
First, we show how to derive sharp stability estimates for linear partially dissipative systems when the algebraic Kalman rank condition (equivalent to the classical Shizuta- Kawashima condition) is satisfied. This linear analysis allows us to establish global-in-time existence and large-time behaviour results in a critical regularity framework for nonlinear partially dissipative hyperbolic systems, using a precise frequency decomposition of the solution via the Littlewood-Paley theory.
Then, we interpret partially dissipative systems as hyperbolic relaxations and study the strong relaxation, in a Lp framework, of the compressible Euler system with damping toward the porous media equation. This is a joint work (Mathematische Annalen ’23) with R. Danchin.
Mon. November 20, 2023 at 14:30H
Nanjing University of Aeronautics and Astronautics
29 Yudao St., Nanjing, Jiangsu Province