CHAPLYGIN EQUATION IN THREE-DIMENSIONAL NON-CONSTANT ISENTROPIC FLOW-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC-PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS(Ⅲ)

This work is the continuation of the discussion of Ref.1].In this Paper we resoive theequations of isentropic gas dynamics into two problems:the three-dimensional non-constant irrotational flow (thus the isentropic flow,too),and the three-dimensional non-constant indivergent flow (i.e.the in compressible isentropic flow).We apply the theory offunctions of a complex variable under Dirac-Pauli representation and the Legendretransformation,transform these equations of two problems from physical space intovelocity space,and obtain two general Chaplygin equations in this paper.The generalChaplygin equation is a linear difference equation,and its general solution can be expressedat most by the hypergeometric functions.Thus we can obtain the general solution of generalproblems for the three-dimensional non-constant isentropic flow of gas dynamics.