Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System

Abstract

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 non-resonant regimes. The results apply to small initial data in scale-invariant Sobolev spaces exhibiting a small amount of angular regularity.

v2: minor typos fixed, few references added, case 2M=m included; v3: minor edits, v4: assumptions rephrased, minor corrections/additions

References in corpus (5)

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• On the 2d Zakharov system with L^2 Schrödinger data
• The cubic Dirac equation: Small initial data in $H^{\frac{1}{2}}({\mathbb{R}}^2)$
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Cited by in corpus (13)

• Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher
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• Global wellposedness for the energy-critical Zakharov system below the ground state
• Conditional large data scattering results for the Dirac-Klein-Gordon system
• The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity
• On the scaling critical regularity of the Yang-Mills system in the Lorenz gauge
• The almost optimal multilinear restriction estimate for hypersurfaces with curvature: the case of $n-1$ hypersurfaces in R^n
• Scattering for the mass-critical nonlinear Klein-Gordon equations in three and higher dimensions
• Global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon system in the Lorenz gauge
• On the radius of spatial analyticity for solutions of the Dirac-Klein-Gordon equations in two space dimensions
• On the scaling critical regularity of the Yang-Mills-Higgs and the Yang-Mills-Dirac system in the Lorenz gauge
• Charge conjugation approach to scattering for the Hartree type Dirac equations with chirality