On the existence of chaos for the ViscousVanWjingaarden Equation

Abstract

We study the viscous van Wijngaarden–Eringen equation which 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 $a_0$ and $\rey_d$, in which we can ensure that this equation admits a uniformly continuous, Devaney chaotic and topologically mixing semigroup on Herzog's type Banach spaces.