学术报告（徐江 2024.11.27）

摘要：The low-frequency assumption has been extensively applied to the large-time asymptotics of solutions to the compressible Navier-Stokes equations and incompressible Navier-Stokes equations since from those classical efforts. In this talk, we will give a sharp decay characterization for the compressible Navier-Stokes equations in the critical framework. Precisely, the Besov boundedness of the low-frequency part of initial perturbation is not only sufficient but also necessary to achieve those upper bounds of time-decay estimates. Furthermore, it is shown that upper and lower bounds of time-decay estimates both hold if and only if the low-frequency part of the initial perturbation belongs to a nontrivial subset of some Besov space. This is a joint work with Brandolese, Shou and Zhang.