research10.1007/s00205-017-1213-1

# Discretely self-similar solutions to the Navier-Stokes equations with Besov space data

## Abstract

We construct self-similar solutions to the three dimensional Navier-Stokes equations for divergence free, self-similar initial data that can be large in the critical Besov space $\dot B^{-1+3/p}_{p,\infty}$ where $3< p< 6$. We also construct discretely self-similar solutions for divergence free initial data in $\dot B^{-1+3/p}_{p,\infty}$ for $3<p<6$ that is discretely self-similar for some scaling factor $\lambda>1$. These results extend those of \cite{BT1} which dealt with initial data in $L^3_w$ since $L^3_w\subsetneq \dot B^{-1+3/p}_{p,\infty}$ for $p>3$. We also provide several concrete examples of vector fields in the relevant function spaces

## Full text

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1703.03480oai:arXiv.org:1703.03480
Last time updated on June 19, 2017View original full text link

This paper was published in arXiv.org e-Print Archive.

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