PARAXIAL APPROXIMATION OF THE VLASOV-MAXWELL SYSTEM: LAMINAR BEAMS

1994 ◽  
Vol 04 (02) ◽  
pp. 203-221 ◽  
Author(s):  
A. NOURI
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Initial Data ◽  
Global Existence ◽  
Local Existence ◽  
Sufficient Conditions ◽  
External Electromagnetic Field ◽  
Evolution System ◽  
Lagrangian Coordinates ◽  
Maxwell System

The Vlasov-Maxwell stationary system for charged particle laminar beams is studied with a paraxial model of approximation. It leads to a degenerate evolution system, which local existence is proved. Then, using lagrangian coordinates, with sufficient conditions on the initial data and the external electromagnetic field, it is shown that global existence is possible.

Classical electrodynamics: the equation of motion

1974 ◽  
Vol 76 (1) ◽  
pp. 359-367 ◽  
Author(s):  
P. A. Hogan
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Scalar Field ◽  
World Line ◽  
External Electromagnetic Field ◽  
Equation Of Motion ◽  
The Self ◽  
Classical Electrodynamics ◽  
Field Equations ◽  
The World

In this paper we derive the Lorentz-Dirac equation of motion for a charged particle moving in an external electromagnetic field. We use Maxwell's electromagnetic field equations together with the assumptions (1) that all fields are retarded and (2) that the 4-force acting on the charged particle is a Lorentz 4-force. To define the self-field on the world-line of the charge we utilize a contour integral representation for the field due to A. W. Conway. This by-passes the need to define an ‘average field’. In an appendix the case of a scalar field is briefly discussed.

scholarly journals Blow-Up of Solutions with High Energies of a Coupled System of Hyperbolic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Jorge A. Esquivel-Avila
Keyword(s):  
Initial Data ◽  
Blow Up ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Coupled System ◽  
Initial Energy ◽  
Evolution System ◽  
High Energies ◽  
Second Order In Time

We consider an abstract coupled evolution system of second order in time. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We compare our results with those in the literature and show how we improve them.

scholarly journals Well-Posedness of the Two-Dimensional Fractional Quasigeostrophic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yongqiang Xu
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Local Existence ◽  
Well Posedness ◽  
Two Dimensional ◽  
Small Initial Data ◽  
General Initial Data ◽  
Local Existence Of Solutions

This paper is concerned with the fractional quasigeostrophic equation with modified dissipativity. We prove the local existence of solutions in Sobolev spaces for the general initial data and the global existence for the small initial data when1/2≤α<1.

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