Sharp decay characterization for compressible flows

Orateur: Ling-Yun SHOU
Localisation: Université d'aéronautique et d'astronautique de Nanjing, Chine
Type: Groupe de travail équations aux dérivées partielles
Site: UPEC
Salle: P1-011
Date de début: 05/02/2024 - 13:45
Date de fin: 05/02/2024 - 14:45

In this talk, we will give a sharp decay characterization of the Cauchy problem for the compressible Navier-Stokes equations in the critical regularity framework. Precisely, we consider the Besov space Bs2,∞ including the case s=d/2 associated with the embedding in L1. We prove that the Bs2,∞ boundedness for the low-frequency part of initial perturbation is not only sufficient but also necessary to achieve upper bounds of time-decay estimates of solutions.  Furthermore, we establish upper and lower bounds of time-decay estimates if and only if the low-frequency part of the initial perturbation belongs to a nontrivial subset of Bs2,∞.