Particles Interacting with a Vibrating Medium: Existence of Solutions and Convergence to the Vlasov--Poisson System
نویسندگان
چکیده
منابع مشابه
Particles Interacting with a Vibrating Medium: Existence of Solutions and Convergence to the Vlasov-Poisson System
We are interested in a kinetic equation intended to describe the interaction of particles with their environment. The environment is modeled by a collection of local vibrational degrees of freedom. We establish the existence of weak solutions for a wide class of initial data and external forces. We also identify a relevant regime which allows us to derive, quite surprisingly, the attractive Vla...
متن کاملGlobal existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting
The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newton...
متن کاملLagrangian Solutions to the Vlasov-poisson System with L Density
The recently developed theory of Lagrangian flows for transport equations with low regularity coefficients enables to consider non BV vector fields. We apply this theory to prove existence and stability of global Lagrangian solutions to the repulsive Vlasov-Poisson system with only integrable initial distribution function with finite energy. These solutions have a well-defined Lagrangian flow. ...
متن کاملLagrangian Solutions to the Vlasov-poisson System with L1 Density
Abstract. The recently developed theory of Lagrangian flows for transport equations with low regularity coefficients enables to consider non BV vector fields. We apply this theory to prove existence and stability of global Lagrangian solutions to the repulsive Vlasov-Poisson system with only integrable initial distribution function with finite energy. These solutions have a well-defined Lagrang...
متن کاملExistence of axially symmetric solutions to the Vlasov-Poisson system depending on Jacobi’s integral
We prove the existence of axially symmetric solutions to the Vlasov– Poisson system in a rotating setting for sufficiently small angular velocity. The constructed steady states depend on Jacobi’s integral and the proof relies on an implicit function theorem for operators.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2016
ISSN: 0036-1410,1095-7154
DOI: 10.1137/16m1065306