Self-similar solutions of the Navier-Stokes equations on weak weighted Lorentz spaces

被引：0
作者：
Hong Liang Li
Jie Cheng Chen
机构：
[1] Zhejiang International Studies University,Department of Mathematics
[2] Zhejiang Normal University,Department of Mathematics
来源：
Acta Mathematica Sinica, English Series | 2015年 / 31卷
关键词：
Navier-Stokes equations; self-similar solutions; convolution; weighted Lorentz spaces; 35Q30; 35Q31; 46E30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the present paper, we prove the existence of global solutions for the Navier-Stokes equations in ℝn when the initial velocity belongs to the weighted weak Lorentz space Λn,∞(u) with a sufficiently small norm under certain restriction on the weight u. At the same time, self-similar solutions are induced if the initial velocity is, besides, a homogeneous function of degree −1. Also the uniqueness is discussed.
引用
收藏
页码：44 / 60
页数：16
相关论文
共 15 条
[1]  
Barraza O A(1996)Self-similar solutions in weak Rev. Mat. Iberoam. 12 411-439
[2]  
Fujita H(1964)-spaces of the Navier-Stokes equations Arch. Rational Mech. Anal. 16 269-315
[3]  
Kato T(1989)On the Navier-Stokes initial value problem, I Comm. Prtial Diff. equations 14 577-618
[4]  
Giga Y(1966)Navier-Stokes flow in ℝ Enseignement Math. 12 249-276
[5]  
Miyakawa T(1984) with measuers as initial voticity and Morrey spaces Math. Z. 187 471-480
[6]  
Hunt R A(1962)On Rend. Sem. Mah. Univ. Padova 32 243-260
[7]  
Kato T(1994)( Comm. Partial Diff. Equations 19 959-1014
[8]  
Kato T(2012)) spaces Georgian Math. J. 19 721-740
[9]  
Fujita H(1998)Strong Quart. J. Math. 49 93-103
[10]  
Kozono H(1963)-solutions of the Navier-Stokes equation in ℝ Duke Math. J. 30 129-142
12