BILINEAR ESTIMATES AND APPLICATIONS TO GLOBAL WELL-POSEDNESS FOR THE DIRAC–KLEIN–GORDON EQUATION ON ℝ1+1

DOI10.1142/S021989161350001XzbMath1284.35356arXiv1202.1967WikidataQ115245234 ScholiaQ115245234MaRDI QIDQ2836508

Timothy Candy

Publication date: 3 July 2013

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.1967

zbMATH Keywords

global well-posednessbilinear estimatesDirac-Klein-Gordon equation

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) PDEs in connection with quantum mechanics (35Q40)

Related Items (6)

Growth of Sobolev norms for the Maxwell–Dirac and Dirac–Klein–Gordon systems in R 1 + 1 ⋮ Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field ⋮ Nonlinear waves and dispersive equations. Abstracts from the workshop held June 26 -- July 2, 2022 ⋮ Sharp ill-posedness of the Dirac-Klein-Gordon system in one dimension ⋮ On the radius of spatial analyticity for the 1d Dirac-Klein-Gordon equations ⋮ Growth-in-time of higher Sobolev norms of solutions to the 1D Dirac–Klein–Gordon system

Cites Work

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• Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension
• One dimensional Dirac equation with quadratic nonlinearities
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• LOW REGULARITY WELL-POSEDNESS OF THE DIRAC–KLEIN–GORDON EQUATIONS IN ONE SPACE DIMENSION
• GLOBAL WELL-POSEDNESS OF THE 1D DIRAC–KLEIN–GORDON SYSTEM IN SOBOLEV SPACES OF NEGATIVE INDEX
• Space‐time estimates for null forms and the local existence theorem
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• Atlas of products for wave-Sobolev spaces on ℝ¹⁺³

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