Evolution of localized asymptotic solutions for linearized Navier — Stokes and MHD equations

All-Russian conference on Nonlinear Waves: Theory and New Applications

Allilueva, A.I.^1,2,3 ; Shafarevich, A.I.^1,2,3,4

Institute for Problems in Mechanics of RAS, Moscow

119526, Russia^1

Moscow Institute of Physics and Technology, State University, Dolgoprudny

141700, Russia^2

National Research Centre Kurchatov Institute, Moscow

123182, Russia^3

Moscow State University, Moscow

119992, Russia^4

关键词: Asymptotic behavior of solutions;    Asymptotic solutions;    Cauchy problems;    External flow;    Initial conditions;    Linearized Navier-Stokes;    Three dimensional space;    Two-dimensional surface;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012046/pdf
DOI  :  10.1088/1742-6596/722/1/012046

来源: IOP

【 摘 要 】

In the paper, the asymptotic behavior of solutions of the Cauchy problem is described for the linearized Navier-Stokes and MHD equations with the initial condition localized in a neighborhood of a two-dimensional surface in three-dimensional space. In particular, conditions for the growth of the perturbation in plane-parallel, two-dimensional, and helical external flows are obtained.