JournalsrmiVol. 12, No. 2pp. 411–439

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

  • Oscar A. Barraza

    Université de Paris Dauphine, Paris, France
Self-similar solutions in weak $L^p$-spaces of the Navier-Stokes equations cover
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Abstract

The most important result stated in this paper is a theorem on the existence of global solutions for the Navier-Stokes equations in Rn\mathbb R^n when the initial velocity belongs to the space weak Ln(Rn)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.

Cite this article

Oscar A. Barraza, Self-similar solutions in weak LpL^p-spaces of the Navier-Stokes equations. Rev. Mat. Iberoam. 12 (1996), no. 2, pp. 411–439

DOI 10.4171/RMI/202