Regularity of weak solutions to a two-dimensional modified Dirac-Klein-Gordon system of equations

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Abstract

We show that solutions to the modified Dirac-Klein-Gordon system in standard notation {Mathematical expression} in two space dimensions with complex-valued initial data ψ(0,x)∈L2 (ℝ2;ℂ4), real valued φ{symbol}(0, x) ∈ W1,2 (ℝ2) and φ{symbol}t (0, x) ∈ L2 (ℝ2) have regularity[Figure not available: see fulltext.] Here g{script}loc1 (ℝ3) denotes the (local) Hardy space, and g(t) is assumed to be in C1(ℝ) and g(0)=0. Consequently nonlinear terms φψ which appear in the classical coupled Dirac-Klein-Gordon system (with the modification g=g(t)∈C1 and g(0)=0) can then be defined in Lloc (ℝ2; L1 (ℝ2)). We hope these results will be useful in establishing the existence of weak solutions to the classical coupled Dirac-Klein-Gordon system in the framework of compensated compactness.

Original languageEnglish (US)
Pages (from-to)67-87
Number of pages21
JournalCommunications In Mathematical Physics
Volume151
Issue number1
DOIs
StatePublished - Jan 1 1993

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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