𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the initial value problem for the Vlasov-Poisson-Fokker-Planck system with initial data in Lp spaces

✍ Scribed by José A. Carrillo; Juan Soler

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
656 KB
Volume
18
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper the global existence of weak solutions for the Vlasov‐Poisson‐Fokker‐Planck equations in three dimensions is proved with an L^1^ ∩ L^p^ initial data. Also, the global existence of weak solutions in four dimensions with small initial data is studied. A convergence of the solutions is obtained to those built by E. Horst and R. Hunze when the Fokker‐Planck term vanishes. In order to obtain the a priori necessary estimates a sequence of approximate problems is introduced. This sequence is obtained starting from a non‐linear regulation of the problem together with a linearization via a time retarded mollification of the non‐linear term. The a priori bounds are reached by means of the control of the kinetic energy in the approximate sequence of problems. Then, the proof is completed obtaining the equicontinuity properties which allow to pass to the limit.

📜 SIMILAR VOLUMES

On the Vlasov–Poisson–Fokker–Planck Equa
On the Vlasov–Poisson–Fokker–Planck Equations with Measures in Morrey Spaces as Initial Data
✍ José A Carrillo; Juan Soler 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 276 KB

In this paper the existence of weak solutions, local and global in time solutions for small initial distribution of particles, for the three-dimensional Vlasov᎐ Poisson᎐Fokker᎐Planck system with measures as initial data is obtained. Also, the uniqueness and stability for these solutions is analysed.

Global weak solutions for the initial–bo
Global weak solutions for the initial–boundary-value problems Vlasov–Poisson–Fokker–Planck System
✍ José A. Carrillo 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 254 KB 👁 2 views

This work is devoted to prove the existence of weak solutions of the kinetic Vlasov-Poisson-Fokker-Planck system in bounded domains for attractive or repulsive forces. Absorbing and reflectiontype boundary conditions are considered for the kinetic equation and zero values for the potential on the bo

Weak solutions of the initial-boundary v
Weak solutions of the initial-boundary value problem for the Vlasov–Poisson system
✍ Naoufel Ben Abdallah 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 979 KB

## Abstract In this paper we show the existence of a weak solution of the boundary value problem for the time dependent Vlasov–Poisson system. First, we regularize the system in order to apply a fixed‐point theorem. Then we pass to the limit using an energy estimate.

On the Galerkin-Method in Intermediate S
On the Galerkin-Method in Intermediate Spaces for the Initial Boundary-Value Problem of the Navier-Stokes Equations in two Dimensions
✍ Michael Böhm 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 429 KB 👁 1 views

We consider a GALERKM scheme for the two-dimensional initial boundary-value problem (P) of the NAVIER-STOKES equations, derive a priori-estimates for the approximations in interpolation spaces between "standard spaces'' as occuring in the theory of weak solutions and obtain well-posedness of (P) wit

On weakly convergent sequences in Banach
On weakly convergent sequences in Banach function spaces and the initial-boundary value problems for non-linear Klein–Gordon–Schrödinger equations
✍ Wang Baoxiang 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 123 KB 👁 2 views

In the paper, we shall prove that almost everywhere convergent bounded sequence in a Banach function space X is weakly convergent if and only if X and its dual space X\* have the order continuous norms. It follows that almost everywhere convergent bounded sequence in ¸N #¸N (1(p , p (R) is weakly co