报告地点：行健楼学术活动室526
Abstract: The L^1 assumption has been extensively applied to study the large-time behavior of solutions to viscous compressible flows since from the celebrated work of Matsumura and Nishida. However, whether the L^1 assumption is sharp for optimal time-decay rates remains open. In this paper, we consider the Besov space \dot{B}^{\sigma}_{2,\infty}, which in particular includes the case \sigma=-d/2 associated with the embedding in L^1. Given a global solution in the critical (minimal regularity) setting, we prove that this Besov boundedness for the low-frequency part of initial perturbation is not only sufficient but also necessary to achieve the upper bounds of time-decay estimates. Furthermore, we establish the upper and lower bounds of time-decay estimates if and only if the low-frequency part of initial perturbation belongs to a nontrivial subset of the Besov space. To the best of our knowledge, our work provides a first result addressing the inverse problem for large-time asymptotics of viscous compressible flows.
