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.
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Communicated by H. Spohn
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Esposito, R., Guo, Y. & Marra, R. Phase Transition in a Vlasov-Boltzmann Binary Mixture. Commun. Math. Phys. 296, 1–33 (2010). https://doi.org/10.1007/s00220-010-1009-8
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DOI: https://doi.org/10.1007/s00220-010-1009-8