On the Dynamics of Navier-Stokes and Euler Equations |
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| Authors: | Yueheng Lan Y. Charles Li |
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| Affiliation: | (1) Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, USA;(2) Present address: Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106-5070, USA;(3) Department of Mathematics, University of Missouri, Columbia, MO 65211, USA |
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| Abstract: | This is a detailed study on certain 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. Due to the difficulty of the problem for the full Navier-Stokes and Euler equations, we also propose and study two simpler models of them. |
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| Keywords: | Heteroclinic orbit Chaos Turbulence Control Melnikov integral Zero viscosity limit Sine-Gordon equation Navier-Stokes equations Euler equations |
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