Japan Journal of Industrial and Applied Mathematics

, Volume 35, Issue 3, pp 1065–1083

# Unimodal solutions of the generalized Constantin–Lax–Majda equation with viscosity

Original Paper Area 1

## Abstract

Steady-states of the generalized Constantin–Lax–Majda equation with the viscosity and an external force are computed numerically by the spectral method. This equation is regarded as a model for two-dimensional turbulent motion of incompressible viscous fluid. We demonstrate numerically that the equation admits unimodal solutions—solutions with one and only one peak and bottom, if the Reynolds number is sufficiently large. We also report some interesting properties of the spectra of unimodal solutions.

## Keywords

Unimodal solution Bifurcation Large Reynolds number flow

65N35 76N99

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© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

## Authors and Affiliations

• Sun-Chul Kim
• 1
• Tomoyuki Miyaji
• 2
• Hisashi Okamoto
• 3
1. 1.Department of MathematicsChung-Ang UniversitySeoulRepublic of Korea
2. 2.Meiji Institute for Advanced Study of Mathematical SciencesMeiji UniversityTokyoJapan
3. 3.Department of MathematicsGakushuin UniversityTokyoJapan