论文标题
Leray对Morrey空间中3D Navier-Stokes方程的向后自相似解决方案
Leray's backward self-similar solutions to the 3D Navier-Stokes equations in Morrey spaces
论文作者
论文摘要
在本文中，显示在那里 不存在非凡的leray向后自相似的解决方案对3D navier-stokes方程，并在Morrey Spaces中配置文件$ \ dot {\ Mathcal {M}}}}^{q，1}（\ Mathbb {rathbb {r} $ \ dot {\ mathcal {m}}}^{q，l}（\ mathbb {r}^{3}）$提供$ 6 \ leq q <\ infty $和$ 2 <l \ l \ leq q $。这概括了Nečas-råužička-šverák[19，acta.math获得的相应结果。 176（1996）] in $ l^{3}（\ mathbb {r}^{3}）$，tsai [25，拱门。配给。机械。肛门。 143（1998）] in $ l^{p}（\ Mathbb {r}^{3}）$，带有$ p \ geq3 $，，Chae-Wolf [3，Arch。配给。机械。肛门。 225（2017）]在lorentz空间中$ l^{p，\ infty}（\ mathbb {r}^{3}）$，带有$ p> 3/2 $，和guevara-phuc [11，siam J. Math。肛门。 12（2018）] in $ \ dot {\ Mathcal {m}}}^{q，\ frac {12-2q} {3}}}}}}}}（\ Mathbb {r}^{3} {3} {3}）$，$ 12/5 \ leq q <3 $ and in $ l^{ $ 12/5 \ leq Q <6 $。
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 $3/2<q<6$, 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 by Nečas-Råužička-Šverák [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 $p>3/2$, 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 $12/5\leq q<6$.
