Multispeed Klein-Gordon systems in dimension three
Yu Deng
TL;DR
This paper proves that small solutions to multispeed Klein-Gordon systems in three spatial dimensions exist globally and behave like linear solutions over time, using new dispersion and oscillatory integral estimates.
Contribution
It introduces improved linear dispersion and bilinear oscillatory integral estimates for multispeed Klein-Gordon systems, extending previous partial results.
Findings
Solutions are globally well-defined and scatter to linear solutions
New dispersion estimates exploit asymptotic spherical symmetry
Bilinear oscillatory integral estimates are developed
Abstract
We consider long time evolution of small solutions to general multispeed Klein-Gordon systems in 3+1 dimensions. We prove that such solutions are always global and scatter to a linear flow, thus extending previous partial results. The main new ingredients of our method is an improved linear dispersion estimate exploiting the asymptotic spherical symmetry of Klein-Gordon waves, and a corresponding bilinear oscillatory integral estimate.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Numerical methods for differential equations