On the existence of chaos for the viscous van Wijngaarden–Eringen equation

• We study chaotic phenomena for acoustic planar propagation.
• The chaos is exhibited in certain spaces of analytic functions.
• This phenomenon is determined by the Knudsen and Reynolds numbers.

We study the viscous van Wijngaarden–Eringen equation: equation(1)∂2u∂t2−∂2u∂x2=(Red)−1∂3u∂t∂x2+a02∂4u∂t2∂x2which corresponds to the linearized version of the equation that models the acoustic planar propagation in bubbly liquids. We show the existence of an explicit range, solely in terms of the constants a0 and Red, in which we can ensure that this equation admits a uniformly continuous, Devaney chaotic and topologically mixing semigroup on Herzog’s type Banach spaces.