Abstract
Stability of planar Coutte flow is investigated by the simplified BGK model. The stationary Navier‐Stokes solutions plus small terms depending on the Knudsen number are used as stationary solutions for the BGK model. The non‐stationary fluctuations for the linearized problem are two dimensional and depend on a coordinate normal to the direction of the flow and the fluctuations of the density are taken not equal to zero. Then the model is truncated on high modes in velocity and coordinate space and the spectral problem is considered. The positive values of the spectrum elements indicate on instability. Also need to mention that the same method will lead to stability in Navier‐Stokes approach.
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