Growth-in-time of higher Sobolev norms of solutions to the 1D Dirac–Klein–Gordon system

DOI10.1142/S0219891619500127zbMath1428.35435OpenAlexW2969951919MaRDI QIDQ5237480

Achenef Tesfahun

Publication date: 18 October 2019

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

Full work available at URL: https://doi.org/10.1142/s0219891619500127

zbMATH Keywords

I-methodgrowth-in-time of Sobolev norms1D DKG

Mathematics Subject Classification ID

Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (3)

Growth of Sobolev norms for the Maxwell–Dirac and Dirac–Klein–Gordon systems in R 1 + 1 ⋮ \(L^\infty\) bounds for Maxwell-gauged equations in \(\mathbb{R}^{1 + 1}\) and their applications ⋮ Remarks on the growth of the Sobolev norms for the Maxwell-Chern-Simons gauged model in \(\mathbb{R}^{1+1}\)

Cites Work

• Unnamed Item
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• A remark on normal forms and the ``upside-down \(I\)-method for periodic NLS: growth of higher Sobolev norms
• Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations on \(S^1\).
• Low regularity global solutions of the Dirac-Klein-Gordon equations in one space dimension.
• Well-posedness for nonlinear Dirac equations in one dimension
• A new proof of global existence for the Dirac Klein-Gordon equations in one space dimension
• Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm
• Remarks on regularity and uniqueness of the Dirac-Klein-Gordon equations in one space dimension
• The Cauchy problem for the 1-D Dirac-Klein-Gordon equation
• Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system
• Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension
• BILINEAR ESTIMATES AND APPLICATIONS TO GLOBAL WELL-POSEDNESS FOR THE DIRAC–KLEIN–GORDON EQUATION ON ℝ¹⁺¹
• 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
• Global Well-posedness Below the Charge Norm for the Dirac-Klein-Gordon System in One Space Dimension

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