Revista Matemática Iberoamericana

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Volume 12, Issue 2, 1996, pp. 411–439
DOI: 10.4171/RMI/202

Published online: 1996-08-31

Self-similar solutions in weak $L^p$-spaces of the Navier-Stokes equations

Oscar A. Barraza[1]

(1) Université de Paris Dauphine, Paris, France

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, an homogeneous function of degree -1. Partial uniqueness is also discussed.

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Barraza Oscar: Self-similar solutions in weak $L^p$-spaces of the Navier-Stokes equations. Rev. Mat. Iberoamericana 12 (1996), 411-439. doi: 10.4171/RMI/202