Title: The Compressible Euler System with Damping: Strong Relaxation Limit in Lᵖ Spaces

Abstract:
In this talk, I will present recent results on the global well-posedness of the compressible Euler system with damping and its relaxation toward the porous medium equation in Lᵖ-based critical spaces, for 2 ≤ p < ∞. Particular emphasis will be placed on the links between this singular relaxation problem, hypocoercive phenomena, and hyperbolic approximations of diffusive systems. We will see that the spectral structure of the linearized dynamics reveals hidden dissipative mechanisms governing both the large-time behavior of solutions and their convergence to the diffusive regime. I will then discuss nonlinear stability and convergence results obtained through a refined Littlewood–Paley frequency analysis.