Global Well-posedness for 3D Generalized Navier-Stokes-Boussinesq Equations  

作　　者：Quan-sen JIU Huan YU 

机构地区：[1]School of Mathematical Sciences,Capital Normal University

出　　处：《Acta Mathematicae Applicatae Sinica》2016年第1期1-16,共16页应用数学学报（英文版）

基　　金：supported by National Natural Sciences Foundation of China(No.11171229,11231006 and 11228102);project of Beijing Chang Chen Xue Zhe

摘　　要：In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate,we prove the global well-posedness for this system with α≥5/4.Moreover,the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization technique.Our results extend ones on the 3D Navier-Stokes equations with fractional diffusion.In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate,we prove the global well-posedness for this system with α≥5/4.Moreover,the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization technique.Our results extend ones on the 3D Navier-Stokes equations with fractional diffusion.

关 键 词：generalized Navier-Stokes-Boussinesq equations global well-posedness uniqueness fourier localization 

分 类 号：O175[理学—数学]