Besov-weak-Herz spaces and global solutions for Navier-Stokes equations (Q1750826)

This is a nice paper on the incompressible Navier-Stokes equations in \(\mathbb{R}^n\), \(n\geq 2\). The authors prove well posedness in critical Besov-weak-Herz spaces which are Besov spaces based on weak-Herz spaces. A basic theory for these spaces is developed. In particular, the authors provide a characterization of these spaces in terms of interpolation of Sobolev-weak-Herz ones. This characterization is the key result in their treatment. Self-similarity and asymptotic behavior of solutions are also addressed.