English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper, it is shown that there  does not exist a non-trivial Leray's backward self-similar solution to the 3DNavier-Stokes equations with profiles in Morrey spaces$\dot{\mathcal{M}}^{q,1}(\mathbb{R}^{3})$ provided $3/2<q<6$, or in$\dot{\mathcal{M}}^{q,l}(\mathbb{R}^{3})$ provided $6\leq q<\infty$ and$2<l\leq q$. This generalizes the corresponding results obtained byNe\v{c}as-R\r{a}u\v{z}i\v{c}ka-\v{S}ver\'{a}k [19, Acta.Math. 176 (1996)] in$L^{3}(\mathbb{R}^{3})$, Tsai [25, Arch. Ration. Mech. Anal. 143 (1998)] in$L^{p}(\mathbb{R}^{3})$ with $p\geq3$,, Chae-Wolf [3, Arch. Ration. Mech. Anal.225 (2017)] in Lorentz spaces $L^{p,\infty}(\mathbb{R}^{3})$ with $p>3/2$, andGuevara-Phuc [11, SIAM J. Math. Anal. 12 (2018)] in$\dot{\mathcal{M}}^{q,\frac{12-2q}{3}}(\mathbb{R}^{3})$ with $12/5\leq q<3$ andin $L^{q, \infty}(\mathbb{R}^3)$ with $12/5\leq q<6$.

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