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

Zoran Grujić

doi:10.3934/dcds.2006.14.837

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2006, Volume 14, Issue 4: 837-843. Doi: 10.3934/dcds.2006.14.837

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

Zoran Grujić^1,

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

Received: December 31, 2004

Revised: September 30, 2005

Published: September 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 35, 76.

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

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