Yosuke Asami | Searcharxiv

arXiv2026

Weighted $L^q$-$L^r$ estimates of a generalized Oseen evolution operator in exterior domains, with applications to the Navier-Stokes flow past a rigid body

We consider a generalized Oseen evolution operator arising from time-dependent rigid motions in 3D exterior domains. Hishida and the present author established the regularity theory of the evolution operator by use of the $L^q$-$L^r$ smoothing estimates with a weight function $(1+|x|)^α$. The objective of this paper is to develop the weighted $L^q$-$L^r$ estimates globally in time. These estimates are applied to the study of the large time behavior of the Navier-Stokes flow around a time-periodic solution in weighted spaces.

math.AP↗

arXiv2025

Regularity properties of a generalized Oseen evolution operator in exterior domains, with applications to the Navier-Stokes initial value problem

Consider a generalized Oseen evolution operator in 3D exterior domains, that is generated by a non-autonomous linearized system arising from time-dependent rigid motions. This was found by Hansel and Rhandi, and then the theory was developed by the second author, however, desired regularity properties such as estimate of the temporal derivative as well as the Hoelder estimate have remained open. The present paper provides us with those properties together with weighted estimates of the evolution operator. The results are then applied to the Navier-Stokes initial value problem, so that a new theorem on existence of a unique strong Lq-solution locally in time is proved.

math.AP↗