Time decay for solutions to the Stokes equations with drift

TL;DR

This paper investigates how Lebesgue norms of solutions to the Stokes equations with drift decay over time, under specific scale-invariant conditions on the drift vector field.

Contribution

It provides new insights into the decay behavior of solutions to the Stokes system with drift, under scale-invariant assumptions on the drift.

Findings

Lebesgue norms decay over time under certain conditions

Scale invariance of the drift influences solution behavior

Results contribute to understanding fluid dynamics with drift

Abstract

In this note, we study the behaviour of Lebesgue norms $\|v(\cdot,t)\|_p$ of solutions $v$ to the Cauchy problem for the Stokes system with drift $u$, which is supposed to be a divergence free smooth vector valued function satisfying a scale invariant condition.