报告题目 Title：Asymptotic instability for the forced Navier-Stokes equations in critical Besov spaces

报告人 Speaker：Mikihiro Fujii

报告人所在单位 Affiliation：Nagoya City University

时间 Time：2025-11-26 10:00-11:00

地点 Venue：Room 1801, Guanghua Eastern Main Tower(Handan Campus)

报告摘要 Abstract：The asymptotic stability is one of the classical problems in the field of mathematical analysis of fluid mechanics. In $\mathbb{R}^n$ with $n \geq 3$, it is easily proved by the standard argument that if the given small external force decays at temporal infinity, then the small forced Navier-Stokes flow also strongly converges to zero as time tends to infinity in the framework of the critical Besov spaces $\dot{B}_{p,q}^{n/p-1}(\mathbb{R}^n)$ with $1 \leq p < n$ and $1 \leq q < \infty$. In this talk, we show that this asymptotic stability fails for $p \geq n$ with $n \geq 3$ in the sense that there exist arbitrary small external forces whose critical Besov norm decays in large time, whereas the corresponding Navier-Stokes flows oscillate and do not strongly converge as $t \to \infty$ in the framework of the critical Besov spaces $\dot{B}_{p,q}^{n/p-1}(\mathbb{R}^n)$. Moreover, we find that the situation is different in the two-dimensional case $n=2$ and show the forced Navier-Stokes flow is asymptotically unstable in $\dot{B}_{p,1}^{2/p-1}(\mathbb{R}^2)$ for all $1 \leq p \leq \infty$. Our instability does not appear in the linear level but is caused by the nonlinear interaction from external forces. This talk is based on the joint work with prof. Hiroyuki Tsurumi (Tokushima University).

个人简介 Bio：Mikihiro Fujii, 名古屋市立大学副教授，博士毕业于九州大学。研究方向为流体力学中偏微分方程的数学理论，特别在Navier-Stokes方程组的适定性与不适定性理论方面做出了创新性的工作，论文发表于Math. Ann., Ann. PDE, Int. Math. Res. Not.等国际知名期刊。

海报 Poster：Mikihiro Fujii 学术报告.jpg