Periodic thermal perturbation in a van der Waals fluid yield chaos: A Mel´nikov function approach

This report discusses the application of the Mel´nikov technique to prove the existence of deterministic chaos in two problems for a van der Waals fluid. The first problem shows that temporal chaos results from small time periodic fluctuations about a subcritical temperature when the fluid is initially quenched into the unstable spinoidal region. The second problem arises from small spatially periodic fluctuation in a tube of fluid if the ambient pressure is appropriately chosen. Complete results may be found in Slemrod & Marsden [1].