摘要
In the present paper, we prove the existence of global solutions for the Navier-Stokes equations in R^n when the initial velocity belongs to the weighted weak Lorentz space A^n,∞ （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.
In the present paper, we prove the existence of global solutions for the Navier-Stokes equations in R^n when the initial velocity belongs to the weighted weak Lorentz space A^n,∞ （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.
基金
Supported by National Natural Science Foundation of China(Grant Nos.11271330,11226069 and 11401530)
Postdoctoral Science Foundation of China(Grant No.2013M531446)
Natural Science Foundation of Zhejiang Province of China(Grant No.LQ13A010018)
Postdoctoral Science Foundation of Zhejiang Province of China(Grant No.Bsh1202060)
