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

  • Sun-Chul Kim
  • Tomoyuki Miyaji
  • Hisashi Okamoto
Original Paper Area 1


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.


Unimodal solution Bifurcation Large Reynolds number flow 

Mathematics Subject Classification

65N35 76N99 



One of the referees kindly let us know the reference [21] and his/her comments are acknowledged to be very useful.


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Copyright information

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

Authors and Affiliations

  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

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