Asymptotic Behavior of the Maxwell-Klein-Gordon system

Abstract

In previous work on the Maxwell-Klein-Gordon system first existence and then decay estimates have been shown. Here we show that the Maxwell-Klein-Gordon in the Lorentz gauge satisfy the "weak null condition" and we give the detailed asymptotics for the scalar field and the potential. These asymptotics have two parts, one wave like along outgoing light cones at null infinity, and one homogeneous inside the light cone at time like infinity. Here the charge plays a crucial role in imposing an oscillating factor in the asymptotic system for the field, and in the null asymptotics for the potential. Similar results have previously been shown for Einstein's equations in wave coordinates, and the Maxwell-Klein-Gordon system apart from being interesting in itself also provides a simpler semilinear model of the quasilinear Enstein's equations.

References in corpus (4)

• Global existence for the Einstein vacuum equations in wave coordinates
• On the asymptotic behavior of solutions to Einstein's vacuum equations in wave coordinates
• Global solution for massive Maxwell-Klein-Gordon equations
• Decay of solutions of Maxwell-Klein-Gordon equations with large Maxwell field

Cited by in corpus (5)

• A local energy estimate for wave equations on metrics asymptotically close to Kerr
• Scattering from Infinity of the Maxwell Klein Gordon Equations in Lorenz Gauge
• Asymptotic completeness for a scalar quasilinear wave equation satisfying the weak null condition
• Timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition
• Scattering for wave equations with sources close to the lightcone and prescribed radiation fields