Cauchy and Goursat problems for the generalized spin zero rest-mass fields on Minkowski spacetime

Abstract In this paper, we study the Cauchy and Goursat problems of spin-$n/2$ zero rest-mass equations on Minkowski spacetime by using conformal geometric method. our strategy, prove wellposedness problem in Einstein's cylinder. Then establish pointwise decays fields energy equalities between null boundaries $\scri^\pm$ hypersurface $\Sigma_0=\left\{ t=0 \right\}$. Finally, partial compactification generalisation H\"ormander's result.