日本航空宇宙学会関西支部分科会「流体力学における現代的アプローチ」講演会

Competing interactions in kinetic models for fluids

Prof. Rossana Marra
(Universita di Roma, "Tor Vergata'', Rome, Italy)

要旨

I will discuss kinetic models modeling systems of particles interacting through potentials which are repulsive and attractive, and the corresponding possible kinds of phase transition.  In particular, I will present a kinetic model for the formation of microemulsion and discuss the microphase separation.

Solution to the Boltzmann equation with non isothermal boundary

Prof. Raffaele Esposito
(M&MOCS - Universita' dell'Aquila, Cisterna di Latina, Italy)

要旨

We consider the Boltzmann equation in an arbitrary container of finite size, on whose walls we prescribe Maxwell diffuse reflection b.c. with non homogeneous temperature. Under the assumption that the variations of the wall temperature are sufficiently small we prove that there is a locally unique stationary solution continuous out of an  explicit singular set which is asymptotically stable with exponential rate. A corollary of these results is a proof of non validity of the Fourier law. The proof of such results is based on new constructive and robust coercivity estimates for the linearized problem.