Decay rates of three dimensional stationary Navier--Stokes flows at the spatial infinity

TL;DR

This paper investigates the decay behavior of solutions to three-dimensional stationary Navier--Stokes equations in critical Besov spaces, establishing well-posedness and decay conditions despite potential singularities.

Contribution

It introduces new well-posedness results in critical Besov spaces and provides decay rate conditions for solutions with singularities.

Findings

Solutions decay at polynomial rates at infinity

Well-posedness established in critical Besov spaces

Conditions for decay despite singularities

Abstract

In this paper, we establish the well-posedness results of the three dimensional stationary Navier--Stokes equations (SNS) in some critical hybrid type Besov spaces with respect to the scaling invariant structure of (SNS). Although such critical functional spaces contain the functions with singularities, we give some sufficient conditions such that the $L^{\infty}$-norm of the solutions of (SNS) decay at the infinity within some polynomial type rate.