Parabolic-scalings on large-time behavior of the incompressible Navier--Stokes flow
arXiv:2410.18452 · doi:10.1016/j.nonrwa.2025.104350
Abstract
Through asymptotic expansion, the large-time behavior of incompressible Navier--Stokes flow in -dimensional whole space is depicted. Especially, from their parabolic scalings, large-time behaviors of any terms on the expansion are clarified. The parabolic scalings also guarantee the uniqueness of the expansion. In the preceding work, the expansion with the th order has already been derived. They also predicted that the flow has some logarithmic evolutions in higher-order decay. In this paper, an asymptotic expansion with th order is presented. Furthermore, logarithmic evolutions are discovered.
14 pages