Nonlinear instability for nonhomogeneous incompressible viscous fluids

作     者：JIANG Fei JIANG Song NI GuoXi 

作者机构：College of Mathematics and Computer ScienceFuzhou University Laboratory of Computational PhysicsInstitute of Applied Physics and Computational Mathematics 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第4期

页      面：665-686页

核心收录：

学科分类：080704[工学-流体机械及工程] 07[理学] 080103[工学-流体力学] 070601[理学-气象学] 08[工学] 0807[工学-动力工程及工程热物理] 0706[理学-大气科学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11101044,11271051,11229101 and 91130020) National Basic Research Program of China (Grant No.2011CB309705) 

主　　题：nonhomogeneous Navier-Stokes equations steady density profile Rayieigh-Taylor instability incompressible viscous flows 

摘      要：We investigate the nonlinear instability of a smooth steady density profile solution to the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field,including a Rayleigh-Taylor steady-state solution with heavier density with increasing height(referred to the Rayleigh-Taylor instability).We first analyze the equations obtained from linearization around the steady density profile *** we construct solutions to the linearized problem that grow in time in the Sobolev space H k,thus leading to a global instability result for the linearized *** the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations,we can then demonstrate the instability of the nonlinear problem in some *** analysis shows that the third component of the velocity already induces the instability,which is different from the previous known results.