Self-similar solutions in weak \(L^ p\)-spaces of the Navier-Stokes equations. (English) Zbl 0860.35092

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.


35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI EuDML