Global existence of Maxwell--Klein--Gordon fields in (2+1)-dimensional spacetime

Journal Article · Fri Aug 01 04:00:00 EDT 1980 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524669· OSTI ID:5326987

Moncrief, V

We study the global existence problem for the Maxwell--Klein--Gordon equations in (2+1)-dimensional, Minkowski spacetime. We first establish local existence, in a suitable Sobolev space, by specializing to the Lorentz gauge and applying standard techniques. We then prove global existence by showing that an appropriate norm of the solutions cannot blow up in a finite time. An essential step in the proof involves showing that a certain second order ''energy'' does not blow up.

• Research Organization: Department of Physics, Yale University, 217 Prospect St. New Haven, Connecticut 06520
• OSTI ID: 5326987
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:8; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
EQUATIONS
GAUGE INVARIANCE
GLOBAL ANALYSIS
INVARIANCE PRINCIPLES
KLEIN-GORDON EQUATION
MATHEMATICAL SPACE
MATHEMATICS
MAXWELL EQUATIONS
MINKOWSKI SPACE
SPACE
SPACE-TIME
WAVE EQUATIONS