Estimates of mild solutions of navier–stokes equations in weak herz-type besov–morrey spaces

Abstract

The main goal of this article is to provide estimates of mild solutions of Navier–Stokes equations with arbitrary external forces in Rn for n ≥ 2 on proposed weak Herz-type Besov–Morrey spaces. These spaces are larger than known Besov–Morrey and Herz spaces considered in known works on Navier–Stokes equations. Morrey–Sobolev and Besov–Morrey spaces based on weak-Herz space denoted as W ˙Kαp,qMsµ and W ˙Kαp,q˙Nsµ,r, respectively, represent new properties and interpolations. This class of spaces and its developed properties could also be employed to study elliptic, parabolic, and conservation-law type PDEs.