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Transference of
bilinear restriction estimates to quadratic variation norms
and the Dirac–Klein–Gordon system
Timothy Candy and Sebastian Herr |
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Vol. 11 (2018), No. 5, 1171–1240
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Abstract |
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Firstly, bilinear Fourier restriction estimates — which are well known for free waves — are extended to adapted spaces of functions of bounded quadratic variation, under quantitative assumptions on the phase functions. This has applications to nonlinear dispersive equations, in particular in the presence of resonances. Secondly, critical global well-posedness and scattering results for massive Dirac–Klein–Gordon systems in dimension three are obtained, in resonant as well as in nonresonant regimes. The results apply to small initial data in scale-invariant Sobolev spaces exhibiting a small amount of angular regularity. |
Keywords
bilinear Fourier restriction, adapted function spaces,
quadratic variation, atomic space, Dirac–Klein–Gordon
system, resonance, global well-posedness, scattering
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Mathematical Subject Classification 2010
Primary: 42B37, 35Q41
Secondary: 42B20, 42B10, 81Q05
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Milestones
Received: 9 May 2017
Revised: 19 October 2017
Accepted: 29 November 2017
Published: 11 April 2018
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Authors |
| Timothy Candy | |
| Universität Bielefeld Fakultät für Mathematik Bielefeld Germany |
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| Sebastian Herr | |
| Universität Bielefeld Fakultät für Mathematik Bielefeld Germany |
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