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

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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.
    Mathematics Subject Classification: Primary: 35, 76.


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