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

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.