On global behavior of solutions of the Maxwell-Klein-Gordon equations

Abstract

It is known that the Maxwell-Klein-Gordon equations in ${\mathbb{R}}^{3+1}$ admit global solutions with finite energy data. In this paper, we present a new approach to study the asymptotic behavior of these global solutions. We show the quantitative energy flux decay of the solutions with data merely bounded in some weighted energy space. We also establish an integrated local energy decay and a hierarchy of $r$-weighted energy decay. The results in particular hold in the presence of large total charge. This is the first result to give a complete and precise description of the global behavior of large nonlinear charged scalar fields.

23pages, 1 figure

References in corpus (6)

• On the quasilinear wave equations in time dependent inhomogeneous media
• Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M
• Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation
• Ultimately Schwarzschildean Spacetimes and the Black Hole Stability Problem
• A geometric approach for sharp Local well-posedness of quasilinear wave equations
• Nonlinear Wave Equations With Null Condition On Extremal Reissner-Nordström Spacetimes I: Spherical Symmetry

Cited by in corpus (2)

• Global solution for massive Maxwell-Klein-Gordon equations
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