Shen Hui-chuan. Chaplygin Equation in Three-Dimensional Non-Constant Isentropic Flow——The Theory of Functions of a Complex Variable under Dirac-Pauli Represen tation and Its Application in Fluid Dynamics(Ⅲ)[J]. Applied Mathematics and Mechanics, 1986, 7(8): 703-712.
 Citation: Shen Hui-chuan. Chaplygin Equation in Three-Dimensional Non-Constant Isentropic Flow——The Theory of Functions of a Complex Variable under Dirac-Pauli Represen tation and Its Application in Fluid Dynamics(Ⅲ)[J]. Applied Mathematics and Mechanics, 1986, 7(8): 703-712.

# Chaplygin Equation in Three-Dimensional Non-Constant Isentropic Flow——The Theory of Functions of a Complex Variable under Dirac-Pauli Represen tation and Its Application in Fluid Dynamics(Ⅲ)

• Received Date: 1985-05-01
• Publish Date: 1986-08-15
• This work is the continuation of the discussion of ref, [1], In this paper we resolve the equations 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 incompressible isentropic flow).We apply the theory of functions of a complez variable under Dirac-Pauli representation and the Legendre transformation,transform these equations of two problems from physical space into velocity space,and obtain two general Chaplygin equations in this paper, The general Chaplygin equation is a linear difference equation,and its general solution can be expressed at most by the hypergeometric functions, Thus we can obtain the general solution of general problems for the three-dimensional non-constant isentropic flow of gas dynamics.
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