Smooth Solutions to the Relativistic Vlasov-Maxwell System
نویسندگان
چکیده
منابع مشابه
Global weak solutions to the relativistic Vlasov-Maxwell system revisited
In their seminal work [3], R. DiPerna and P.-L. Lions established the existence of global weak solutions to the Vlasov-Maxwell system. In the present notes we give a somewhat simplified proof of this result for the relativistic version of this system, the main purpose being to make this important result of kinetic theory more easily accessible to newcomers in the field. We show that the weak so...
متن کاملGlobal Weak Solutions to the Relativistic Vlasov - Maxwell System Revisited 1
Abstract. In their seminal work [3], R. DiPerna and P.-L. Lions established the existence of global weak solutions to the Vlasov-Maxwell system. In the present notes we give a somewhat simplified proof of this result for the relativistic version of this system, the main purpose being to make this important result of kinetic theory more easily accessible to newcomers in the field. We show that t...
متن کاملOn the Controllability of the Relativistic Vlasov-maxwell System
In this paper, we study the controllability of the two-dimensional relativistic Vlasov-Maxwell system in a torus, by means of an interior control. We give two types of results. With the geometric control condition on the control set, we prove the local exact controllability of the system in large time. Our proof in this case is based on the return method, on some results on the control of the M...
متن کاملThe Darwin Approximation of the Relativistic Vlasov-Maxwell System
We study the relativistic Vlasov-Maxwell system which describes large systems of particles interacting by means of their collectively generated forces. If the speed of light c is considered as a parameter then it is known that in the Newtonian limit c → ∞ the Vlasov-Poisson system is obtained. In this paper we determine the next order approximate system, which in the case of individual particle...
متن کاملDistributional solutions to the Maxwell-Vlasov equations
The distributional form of the Maxwell-Vlasov equations are formulated. Submanifold distributions are analysed and the general submanifold distributional solutions to the Vlasov equations are given. The properties required so that these solutions can be a distributional source to Maxwell’s equations are analysed and it is shown that a sufficient condition is that spacetime be globally hyperboli...
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: Communications in Mathematical Sciences
سال: 2007
ISSN: 1539-6746,1945-0796
DOI: 10.4310/cms.2007.v5.n5.a7