Temporal decay estimates for global solutions of the Navier-Stokes equations with the Coriolis force

TL;DR

This paper establishes decay estimates for global solutions of the Navier-Stokes equations with Coriolis force, showing they decay faster than heat flow under certain conditions across all L^p norms.

Contribution

It provides new decay rate estimates for solutions with Coriolis force, extending understanding of their long-term behavior in various norms.

Findings

Solutions decay as fast as linearized solutions under small initial data.

Decay rates are higher than those predicted by heat equation flow.

Estimates hold for all L^p norms with p in [2, ∞].

Abstract

We consider temporal decay estimates for global solutions of the Navier-Stokes equations with the Coriolis force. We show that under several conditions including the smallness of the initial data, the solution decays as fast as the corresponding linearized solutions, and its decay rate is higher than expected from the flow of the heat equation. The estimates are derived for all $L^p$-norms with $p\in[2, \infty].$