Regularity of forward-in-time self-similar solutions to the 3D Navier-Stokes equations

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October 2006, 14(4): 837-843. doi: 10.3934/dcds.2006.14.837

Regularity of forward-in-time self-similar solutions to the 3D Navier-Stokes equations

1.	Department of Mathematics, University of Virginia, Charlottesville, VA 22904, United States

Received January 2005 Revised October 2005 Published January 2006

Abstract
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Any forward-in-time self-similar (localized-in-space) suitable weak solution to the 3D Navier-Stokes equations is shown to be infinitely smooth in both space and time variables. As an application, a proof of infinite space and time regularity of a class of a priori singular small self-similar solutions in the critical weak Lebesgue space $L^{3,\infty}$ is given.

Keywords: Navier-Stokes equations, self-similar solutions., regularity.

Mathematics Subject Classification: Primary: 35, 7.

Citation: Zoran Grujić. Regularity of forward-in-time self-similar solutions to the 3D Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 837-843. doi: 10.3934/dcds.2006.14.837

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