論文內容主要是把D-K-G在2+1維上的Quadratic null form estimate 做詳細的證明

The purpose of my paper is to fill up the quadratic null form estimate of D-K-G equations.

[Ba] A.Bachelot Global existence of large amplitude solutions
for Dirac-Klein-Gordon systems in Minkowski spaceLecture Notes
in Math. 1402(1989)pp. 99-113, Springer,Berlin.

[Be] Beals,M. Self-spreading and strength of
singularities for solutions to semilinear wave equations.Ann. of
Math.118(1983)187-214.

[Bo] N.Bournaveas Low regularity solutions of the
Dirac-Klein-Gordon equations in two space dimensionsComm. PDE
26,2001 pp.1345-1366.

[BL] J.Bergh & J.Lofstrom Interpolation Spaces,An
Introduction Springer-Verlag, Berlin, Heidelberg, New York 1976.

[CG] J.Chadam & R.Glassey On the Maxwell-Dirac equations
with zero magnetic field and their solutions in two space
dimensions J. Math. Anal. Appl. 53, 1976 pp. 495-507.

[F1] Yung-fu Fang Local Existence for Semilinear Wave
Equations and Applications to Yang-Mills Equations Ph.D
dissertation, 1996, University of Maryland, College Park.

[F2] Yung-fu Fang A Direct Proof of Global Existence for the
Dirac-Klein-Gorgon Equations in One Space Dimension, Taiwanese
Journal of Math. 2004.

[FG] Yung-fu Fang & Manoussos Grillakis On the
Dirac-Klein-Gordon system in 2+1 dimensions preprint, 2004.

[G] V. Georgiev Small amplitude solutions of the
Maxwell-Dirac equations Indiana Univ. Math. J. 40, 1991
pp.845-883.

[GS] R. Glassey & W. Strauss Conservation laws for the
classical Maxwell-Dirac and Klein-Gordon-Dirac equations J. Math.
Phys. 20, 1979 pp. 454-458.

[K] S. Klainerman Mathematical Theory of Classical Fields and
General relativity Mathematical Physics X 1991, Proceedings,
Leipzig, Germany.

[KM] S. Klainerman & M. Machedon Space-time estimates for
null forms and the local existence theorem Comm. Pure Appl. Math.
XLVI 1993 pp. 1221-1268.

[S] E. M. Stein Harmonic Analysis: Real-Variable Methods,
Orthogonality, and Oscillatory integrals Princeton Univ. Press,
Princeton, New Jersey 1993.

[Z] Y. Zheng Regularity of week solutions to a
two-dimensional modified Dirac-Klein-Gordon system of equations
Commun. Math. Phys. 151,1993pp.67-87

[C] J. Chadam, Global Solutions of the Cauchy Problem for the
(Classical) Coupled Maxwell-Dirac Equations in one Space dimension
, J. Funct. Anal.13 1973, pp. 173-184.