Loading...
Please wait, while we are loading the content...
Similar Documents
Nonlinear Instability of Ideal Plane Flows
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lin, Zhiwu |
| Copyright Year | 2004 |
| Abstract | We study nonlinear instability of stationary ideal plane ows. For any bounded domain and very general steady ows, we showed that if the linearized equation has an exponentially growing solution then the steady ow is nonlinearly unstable. The nonlinear instability is in the sense that we can nd an initial perturbation arbitrarily close to the steady ow such that the Lp norm of the velocity perturbation grows exponentially beyond a xed value. The same result is also proved for the Charney-Hasegawa-Mima equation. 1. Introduction We consider a two-dimensional incompressible inviscid ow satisfying Euler equations (1.1a) @tu+ (u ru) +rp = 0; (1.1b) r u = 0; in a bounded domain of class C with boundary @ composed of a nite number of connected components i. The boundary condition is (1.1c) u n = 0 on @ ; where n stands for the unit outer normal of @ . The vorticity form of (1.1) is given by (1.2) @t! + curl 1 (!) r! = 0; where u=curl ! is de ned for given circulations I |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://people.math.gatech.edu/~zlin/publication/euler-nonlinear.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Blood Circulation Connected component (graph theory) Control theory Euler Flow Instability Navier–Stokes equations Nonlinear programming Nonlinear system Normal (geometry) Stationary process Unstable Medical Device Problem Velocity (software development) cURL |
| Content Type | Text |
| Resource Type | Article |
