Phase Transition in a Vlasov-Boltzmann Binary Mixture

Abstract

There are not many kinetic models where it is possible to prove bifurcation phenomena for any value of the Knudsen number. Here we consider a binary mixture over a line with collisions and long range repulsive interaction between different species. It undergoes a segregation phase transition at sufficiently low temperature. The spatially homogeneous Maxwellian equilibrium corresponding to the mixed phase, minimizing the free energy at high temperature, changes into a maximizer when the temperature goes below a critical value, while non homogeneous minimizers, corresponding to coexisting segregated phases, arise. We prove that they are dynamically stable with respect to the Vlasov-Boltzmann evolution, while the homogeneous equilibrium becomes dynamically unstable.

References in corpus (1)

• Displacement convexity and minimal fronts at phase boundaries

Cited by in corpus (5)

• The McKean-Vlasov Equation in Finite Volume
• Boltzmann Equation with a Large Potential in a Periodic Box
• The initial boundary value problem for the Boltzmann equation with soft potential
• The Vlasov-Poisson-Boltzmann system for a disparate mass binary mixture
• Instability in a Vlasov-Fokker-Planck binary mixture