A weakly nonlinear Landau model for compressible Kelvin-Helmholtz instability is proposed, but its coefficients are not derived and the linearized base flow lacks the shear that creates the instability.
Chandrasekhar ,\ https://cmc.marmot.org/Record/.b27674666 title Hydrodynamic and Hydromagnetic Stability \ ( publisher Oxford University Press ,\ year 1961 ) NoStop
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Nonlinear Stability and Dynamics of Supersonic Compressible Flows
A weakly nonlinear Landau model for compressible Kelvin-Helmholtz instability is proposed, but its coefficients are not derived and the linearized base flow lacks the shear that creates the instability.