Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On unstable and neutral spectra of incompressible inviscid and viscid fluids on the $ 2$D torus

Author: Vincent Xiaosong Liu
Journal: Quart. Appl. Math. 53 (1995), 465-486
MSC: Primary 76D05; Secondary 35Q30, 76E05, 76N10
DOI: https://doi.org/10.1090/qam/1343462
MathSciNet review: MR1343462
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Abstract: We completely determine all the unstable modes and neutral modes for the Kolmogorov flow $ \left( \sin \left( 2{x_2} \right), 0 \right)$ on the two-dimensional torus $ \left[ 0, 2\pi \right] \times \left[ 0, 2\pi \right]$ for both the Navier-Stokes equations and the Euler equations. We also give comments on ``vorticity generation".

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DOI: https://doi.org/10.1090/qam/1343462
Article copyright: © Copyright 1995 American Mathematical Society

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