本篇論文主要在探討2+1維Dirac-Klein-Gordon Equation問題的研究。我們利用疊代法，以及透過解的形式的傅立葉轉換，分別對其5個部分作估計，得出滿足contraction的條件，再利用Fixed Point Theorem得到局部解的存在，最後再利用守恆律得到通解，就得出我們要的結果。

In these years , the main work of mine is to deal with the Cauchy problem for the Dirac-Klein-Gordon equation in 2+1 dimensions. We could prove the Cauchy problem has the local and global solutions through the satisfying of some　conditions. The conditions consist of some estimates and the using of the fixed point argument. So , in this paper , we also demonstrate the estimate of each part of the term.

[B]　J.Bourgain　,　Invariant Measures for NLS in Infinite Volume　,　Commun.Math.Phys.　210　,　605-620　,　(2000).
[Ba]　A.Bachelot　,　Global existence of large amplitude solutions for Dirac-Klein-Gordon systems in Minkowski space　,　Lecture Notes in Math.　1402　,　99-113(Springer Berlin)　,　(1989).
[Bo]　N.Bournaveas　,　A new proof of global existence for the Dirac-Klein-Gordon equation in one space dimension　,　J.Funct. Anal.　173　,　203-213　,　(2000).
[C]　 J.Chadam　,　Global Solutions of the Cauchy Problem for the (Classical) Coupled Maxwell-Dirac Equations in one Space Dimension　,　J. Funct. Anal.　13　,　173-184　,　(1973).
[CG]　J.Chadam and R.Glassey　,　On Certain Global Solutions of the Cauchy Problem for the (Classical) Coupled Klein-Gordon-Dirac equations in one and three Space Dimensions　,　Arch. Rational Mech. Anal.　54　,　223-237　,　(1974).
[F1]　Yung-fu Fang　,　Local Existence for Semilinear Wave Equations and Applications to Yang-Mills Equations　,　Ph.D dissertation (University of Maryland)　,　(1996).
[F2]　Yung-fu Fang　,　Existence and Uniqueness for Dirac-Klein-Gordon Equations in One Space Dimension　,　(2002)(preprint)
[F3]　Yung-fu Fang　,　A Direct Proof of Global Existence for the Dirac-Klein-Gordon Equations in One Space Dimension　,　Taiwanese Journal of Math　,　(2004).
[FG]　Yung-fu Fang and Manoussos Grillakis　,　Existence and Uniqueness for Boussinesq type Equations on a Circle　,　Comm. PDE 21　,　1253-1277　,　(1996).
[G]　V. Georgiev　,　Small amplitude solutions of the Maxwell-Dirac equations　,　Indiana Univ. Math. J. 40　,　845-883　,　(1991).
[GS]　R.Glassey and W. Strauss　,　Conservation laws for the classical Maxwell-Dirac and Klein-Gordon-Dirac equations　,　J. Math. Phys. 20　,　454-458　,　(1979)
[KM]　S. Klainerman and M.Machedon　,　Space-time estimates for null forms and the local existence theorem　,　Comm. Pure Appl. Math. XLVI　,　1221-1268　,　(1993).
[KU]　Sergej Kuksin　,　Infinite-Dimensional Symplectic Capacities and a Squeezing Theorem for Hamiltonian PDE's　,　Commun. Math. Phys 167　,　531-552　,　(1995).
[S]　E.M. Stein　,　Singular Integrals and Differentiability Properties of　Functions　,　Princeton University Press　,　(1970).
[Z]　Y. Zheng　,　Reqularity of weak solutions to a two-dimensional modified Dirac-Klein-Gordon system of equations　,　Commun. Math. Phys. 151　,　67-87　,　(1993).