Self-similar solutions in weak \(L^ p\)-spaces of the Navier-Stokes equations (Q1923684)

Summary: The most important result stated in this paper is a theorem on the existence of global solutions for the Navier-Stokes equations in \(\mathbb{R}^n\) when the initial velocity belongs to the space weak \(L^n (\mathbb{R}^n)\) with a sufficiently small norm. Furthermore, this fact leads us to obtain self-similar solutions if the initial velocity is, besides, a homogeneous function of degree \(-1\). Partial uniqueness is also discussed.