On the Dynamics of Navier-Stokes and Euler Equations

Details On the Dynamics of Navier-Stokes and Euler Equations On the Dynamics of Navier-Stokes and Euler Equations

2006-11-10

arxiv.org/abs/nlin/0611021v1

Nonlinear Sciences

Chaotic Dynamics

53 pages, 39 figures

Scientific paper

This is a rather comprehensive study on the dynamics of Navier-Stokes and Euler equations via a combination of analysis and numerics. We focus upon two main aspects: (a). zero viscosity limit of the spectra of linear Navier-Stokes operator, (b). heteroclinics conjecture for Euler equation, its numerical verification, Melnikov integral, and simulation and control of chaos. Besides Navier-Stokes and Euler equations, we also study two models of them.

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