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arXiv · 2006.15776

Leray's backward self-similar solutions to the 3D Navier-Stokes equations in Morrey spaces

Quansen Jiu·Yanqing Wang·Wei Wei
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Abstract

In this paper, it is shown that there does not exist a non-trivial Leray's backward self-similar solution to the 3D Navier-Stokes equations with profiles in Morrey spaces $\dot{\mathcal{M}}^{q,1}(\mathbb{R}^{3})$ provided $3/2 3/2$, and Guevara-Phuc [11, SIAM J. Math. Anal. 12 (2018)] in $\dot{\mathcal{M}}^{q,\frac{12-2q}{3}}(\mathbb{R}^{3})$ with $12/5\leq q<3$ and in $L^{q, \infty}(\mathbb{R}^3)$ with $12/5\leq q<6$.

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Quansen Jiu, Yanqing Wang, Wei Wei. 2020-06-29. Leray's backward self-similar solutions to the 3D Navier-Stokes equations in Morrey spaces. https://arxiv.org/abs/2006.15776

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