## 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)∈L^{2} (ℝ^{2};ℂ^{4}), real valued φ{symbol}(0, x) ∈ W^{1,2} (ℝ^{2}) and φ{symbol}_{t} (0, x) ∈ L^{2} (ℝ^{2}) have regularity[Figure not available: see fulltext.] Here g{script}_{loc}^{1} (ℝ^{3}) denotes the (local) Hardy space, and g(t) is assumed to be in C^{1}(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)∈C^{1} and g(0)=0) can then be defined in L_{loc}^{∞} (ℝ^{2}; L^{1} (ℝ^{2})). 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 language | English (US) |
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Pages (from-to) | 67-87 |

Number of pages | 21 |

Journal | Communications In Mathematical Physics |

Volume | 151 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1993 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics