Pointwise decay in space and in time for incompressible viscous flow around a rigid body moving with constant velocity

TL;DR

This paper establishes pointwise decay estimates over space and time for solutions to the Oseen and Navier-Stokes systems in 3D, providing insights into their long-term behavior around a moving rigid body.

Contribution

It introduces new pointwise decay estimates for the velocity field in the time-dependent Oseen and Navier-Stokes systems with boundary conditions, advancing understanding of flow stability.

Findings

Decay estimates for velocity solutions in 3D

Results applicable to flows around moving bodies

Enhanced understanding of flow stability and asymptotics

Abstract

We present pointwise space-time decay estimates for the velocity part of solutions to the time-dependent Oseen system in 3D, with Dirichlet boundary conditions and vanishing velocity at infinity. In addition, similar estimates are derived for solutions to the time-dependent incompressible Navier-Stokes system with Oseen term, and for solutions to the stability problem associated with the stationary incompressible Navier-Stokes system with Oseen term.