Ill-posedness of the Thirring model below the critical regularity

DOI10.1063/1.5124096zbMath1454.81074arXiv1906.02251OpenAlexW3100648236MaRDI QIDQ5140940

Achenef Tesfahun, Sigmund Selberg

Publication date: 17 December 2020

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.02251

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Ill-posed problems for PDEs (35R25) NLS equations (nonlinear Schrödinger equations) (35Q55) Spinor and twistor methods applied to problems in quantum theory (81R25) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Critical points and critical submanifolds in differential topology (57R70)

Cites Work

• The cubic Dirac equation: small initial data in \({H^{\frac{1}{2}}(\mathbb R^2)}\)
• Global strong solution to the Thirring model in critical space
• Global existence for an \(L^2\) critical nonlinear Dirac equation in one dimension
• A soluble relativistic field theory
• Long range scattering for the cubic Dirac equation on \(\mathbb{R}^{1+1}\).
• Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field
• Nonexistence of self-similar blowup for the nonlinear Dirac equations in \((1+1)\) dimensions
• The cubic Dirac equation: small initial data in \(H^1(\mathbb R^3)\)
• Low regularity well-posedness for Gross-Neveu equations
• L²orbital stability of Dirac solitons in the massive Thirring model
• Global Solutions of the Cauchy Problem for the (Classical) Coupled Maxwell-Dirac and Other Nonlinear Dirac Equations in One Space Dimension
• Global Well-Posedness for the Massless Cubic Dirac Equation: Table 1

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