Scattering theory for the Dirac equation of Hartree type in \(2+1\) dimensions

DOI10.1016/j.na.2009.05.059zbMath1239.35130OpenAlexW1998622646MaRDI QIDQ425840

Kimitoshi Tsutaya, Shuji Machihara

Publication date: 9 June 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.05.059

zbMATH Keywords

Dirac equationscattering problemHartree typecritical Sobolev space

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Scattering theory for PDEs (35P25) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (2)

Scattering theory for the Dirac equation of Hartree type and the semirelativistic Hartree equation ⋮ Small data scattering of 2d Hartree type Dirac equations

Cites Work

• Local well-posedness for a nonlinear Dirac equation in spaces of almost critical dimension
• On the Maxwell-Dirac equations with zero magnetic field and their solution in two space dimensions
• Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation.
• An overview on linear and nonlinear Dirac equations
• On the existence of weak solutions for a nonlinear time dependent Dirac equation
• Endpoint Strichartz estimates
• A Semilinear Dirac Equation inH^s(R³) fors> 1
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