Estimates of time-periodic fundamental solutions to the linearized Navier-Stokes equations

TL;DR

This paper investigates fundamental solutions to the time-periodic linearized Navier-Stokes equations, establishing their integrability and pointwise estimates in multiple dimensions, which aids in understanding fluid flow behaviors.

Contribution

It provides new integrability properties and pointwise estimates for fundamental solutions of the time-periodic linearized Navier-Stokes equations, expanding theoretical understanding.

Findings

Established integrability properties of solutions.

Derived pointwise estimates for fundamental solutions.

Extended analysis to multiple spatial dimensions.

Abstract

Fundamental solutions to the time-periodic Stokes and Oseen linearizations of the Navier-Stokes equations in dimension $n\geq 2$ are investigated. Integrability properties and pointwise estimates are established.