Time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space with a non-zero drift term: Asymptotic profile at spatial infinity

TL;DR

This paper derives the asymptotic behavior at spatial infinity of weak time-periodic solutions to the 3D Navier-Stokes equations with a drift, explicitly identifying the profile via the Oseen fundamental solution.

Contribution

It provides the first explicit asymptotic expansion for time-periodic solutions with a drift in the whole space, including a pointwise estimate for the remainder.

Findings

Explicit asymptotic profile expressed via Oseen fundamental solution

Pointwise estimate for the remainder term

Asymptotic behavior characterized at spatial infinity

Abstract

An asymptotic expansion at spatial infinity of a weak time-periodic solution to the Navier-Stokes equations with a non-zero drift term in the three-dimensional whole-space is carried out. The asymptotic profile is explicitly identified and expressed in terms of the well-known Oseen fundamental solution. A pointwise estimate is given for the remainder term.