重力场中Navier-Stokes方程的线性不稳定性  

The Linear Instability of the Gravity Driven Viscous Navier-Stokes Flow in Three-dimensional

作　　者：杨静[1] 葛晴 李吉娜[1] ANG Jing;GE Qing;LI Ji-na(College of Science,Zhongyuan University of Technology,Zhengzhou 450007,China)

机构地区：[1]中原工学院理学院

出　　处：《数学的实践与认识》2019年第23期171-176,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11701594);河南省高等学校重点科研项目(17A110037,18A110036,18A110038)

摘　　要：研究了三维不可压粘性Navier-Stokes方程的线性不稳定性.即当流体处在重力场时,若稳态密度有一定的连续性并随着高度的增加而增加时(即Rayleigh-Taylor密度),重力场中的Navier-Stokes流体是线性不稳定的.利用变分法解出线性方程的线性不稳定解.We investigate the instability of some steady-states of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity.When the steady density is heavier with increasing height(i.e.,the Rayleigh-Taylor steady-state),we show that the steady-state is linear unstable.by constructing a(standard) energy functional and exploiting the modified variational method.

关 键 词：NAVIER-STOKES方程 稳态密度 变分方法 

分 类 号：O17[理学—数学]