No abstract

No abstract

Abstract. We present the global existence and stability of mild solutions to the Boltzmann system with inverse power molecular interactions for a binary gas mixture, when initial data are sufficiently small and decay exponentially in phase space. For the existence and stability of mild solutions, we employ a modified Kaniel-Shinbrot's scheme and a weighted nonlinear functional approach. Time-asymptotic convergence toward the free molecular motion is established using a weighted collision potential, and we show that the weighted L 1 -distance between two mild solutions is uniformly controlled by that of initial data.1. Introduction. This paper is devoted to the global existence and stability of mild solutions to the Boltzmann system for a binary gas mixture in a near free molecular regime, which is a perturbation of a background vacuum state. Consider the dynamics of a dilute binary gas mixture consisting of two neutral species A and B. In kinetic theory, the dynamics of dilute gases are effectively described by velocity moments of the velocity distribution function. We denote by F A and F B the velocity distribution functions of species A and B respectively. Then the spatial-temporal evolution of these

We present the global existence and long-time behavior of measurevalued solutions to the kinetic Kuramoto-Daido model with inertia. For the global existence of measure-valued solutions, we employ a Neunzert's meanfield approach for the Vlasov equation to construct approximate solutions. The approximate solutions are empirical measures generated by the solution to the Kuramoto-Daido model with inertia, and we also provide an a priori local-in-time stability estimate for measure-valued solutions in terms of a bounded Lipschitz distance. For the asymptotic frequency synchronization, we adopt two frameworks depending on the relative strength of inertia and show that the diameter of the projected frequency support of the measure-valued solutions exponentially converge to zero.