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arXiv · 1509.08177

Leray's self-similar solutions to the Navier--Stokes equations with profiles in Marcinkiewicz and Morrey spaces

Cristi Guevara·Nguyen Cong Phuc
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Abstract

We rule out the existence of Leray's backward self-similar solutions to the Navier--Stokes equations with profiles in $L^{12/5}(\R^3)$ or in the Marcinkiewicz space $L^{q,\infty}(\R^3)$ for $q\in(12/5, 6)$. This follows from a more general result formulated in terms of Morrey spaces and the first order Riesz's potential.

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Cristi Guevara, Nguyen Cong Phuc. 2015-09-28. Leray's self-similar solutions to the Navier--Stokes equations with profiles in Marcinkiewicz and Morrey spaces. https://arxiv.org/abs/1509.08177

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