Models of Particles of the Michie–King Type

In this paper we study the model of the Michie–King distribution of the self-gravitating system of diffusive particles. This leads to the pressure function of the Michie–King type, being the alternative to the Maxwell–Boltzmann and Fermi–Dirac statistics. The most recent considerations of such systems were suggested by de Vega et al. and Chavanis et al. We consider the existence vs blow-up depending on mass M and the temperature θ of the system. In the two dimensional case 8 π is the threshold value for the M / θ for the classical Michie–King model exactly like in the Maxwell–Boltzmann case. Related systems appear in models of chemotaxis and description of 2-D Euler vortices.