GLOBAL WELL-POSEDNESS OF THE 1D DIRAC–KLEIN–GORDON SYSTEM IN SOBOLEV SPACES OF NEGATIVE INDEX

DOI10.1142/S0219891609001952zbMath1193.35165arXiv0809.1164OpenAlexW2963849545MaRDI QIDQ3647645

Achenef Tesfahun

Publication date: 23 November 2009

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

Full work available at URL: https://arxiv.org/abs/0809.1164

zbMATH Keywords

global well-posednessDirac-Klein-Gordon equations\(I\)-method

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) PDEs in connection with quantum mechanics (35Q40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

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 ⋮ Global well-posedness of the Maxwell-Dirac system in two space dimensions ⋮ Remarks on regularity and uniqueness of the Dirac-Klein-Gordon equations in one space dimension ⋮ Global Solutions for the Dirac–Klein–Gordon System in Two Space Dimensions ⋮ 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 ⋮ BILINEAR ESTIMATES AND APPLICATIONS TO GLOBAL WELL-POSEDNESS FOR THE DIRAC–KLEIN–GORDON EQUATION ON ℝ¹⁺¹ ⋮ Growth-in-time of higher Sobolev norms of solutions to the 1D Dirac–Klein–Gordon system

Cites Work

• A new proof of global existence for the Dirac Klein-Gordon equations in one space dimension
• The Cauchy problem for the 1-D Dirac-Klein-Gordon equation
• Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension
• Global Well-Posedness for Schrödinger Equations with Derivative
• LOW REGULARITY WELL-POSEDNESS OF THE DIRAC–KLEIN–GORDON EQUATIONS IN ONE SPACE DIMENSION
• BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS
• Low regularity solutions for a class of nonlinear wave equations
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋