信阳师范学院学报（自然科学版）2016，Vol.29Issue(3)：340-343,4.DOI:10.3969/j.issn.1003-0972.2016.03.008
一个超临界高耗散三维 Navier-Stokes 方程的整体解
Global Solution for a Supercritical Hyper-dissipative Three-dimensional Navier-Stokes Equation
摘要
Abstract
The global regularity of the supercritical hyper-dissipative three-dimensional Navier-Stokes equa-tion in the whole space was studied.This model modified the dissipation term in the classical Navier-Stokes e-quation,and the dissipative termΔu here is replaced by-D 2 u ,where D is a Fourier multiplier.The global reg-ularity of the critical and supercritical high dissipative case of Navier-Stokes equation was proved when the sym-bol is m (ξ)=|ξ|α,α≥ 5/4.This slightly by establishing global regularity under the condition that m (ξ)=|ξ|α/g (|ξ|)for all sufficiently largeξand some nondecreasing function g :R+→ R+ such that∫¥ 1 ds/(sg (s )4 )= +¥were improved.By the classical energy method,the global regularity of the model was proved in a slightly weaker condition.关键词
Navier-Stokes 方程/超临界/整体正则性/爆破准则/能量估计Key words
Navier-Stokes equation/supercritical/global regularity/blow-up criterion/energy estimation分类
数理科学引用本文复制引用
张士勤,葛玉丽..一个超临界高耗散三维 Navier-Stokes 方程的整体解[J].信阳师范学院学报（自然科学版）,2016,29(3):340-343,4.基金项目
河南省自然科学基金项目(132300410440,132300410211) （132300410440,132300410211）
