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On the Dynamics of Navier-Stokes and Euler Equations

Yueheng Lan·Y. Charles Li
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Abstract

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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Yueheng Lan, Y. Charles Li. 2006-11-10. On the Dynamics of Navier-Stokes and Euler Equations. https://arxiv.org/abs/nlin/0611021

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