Abstract
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. c. the in compressible isentropic flow). We apply the theory of functions of a complex 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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References
Shen Hui-chuan, The theory of functions of a complex variable under Dirac-Pauli representation and its application in fluid dynamics (1),Appl. Math. Mech.,7, 4 (1986).
Shen Hui-chuan, The general solution of peristaltic fluid dynames,Nature Journal 7, 10 (1984), 799;7, 12 (1984), 940. (in Chinese)
Tsien Hsue-shen,Fundamentals of Gas Dynamics (ed. by H. W. Emmons), section A:Equations of Gas Dynamics, Oxford Univ. (1958).
Landau, L. D., and E. M. Lifshitz,Continuum Nechames, Mational, Moscow (1954), (in Russian);Fluid Mechanics, Pergamon (1975).
Böhm, D., A suggested interpretation of the quantum theory in terms of “Hidden” variables.Phys. Rev.,85 (1952), I. 166–179; 11. 180–193.
Taniuti, T. and K. Nishihara,Nonlinear Waves, Pitaman. (1983).
Eckhaus, W. and A Van Harten,The Inverse Scattering Transformation and the Theory of Solitons an Introduction Mathematics Studies 50, North-Holland (1981).
Oswatitsch, K.,Gas. Dynamics, Academic (1956).
Chaplygin, C. A., Über gasstrahlen, Wiss. Ann. Univ.,Moskau Math. Phys.,21 (1904), 1–121; or NACA TM 1063.
Ringleb, F., Lösungen der differentialgleichung einer adiabatischen strömung,ZAMM 20 (1940), 185–198.
Shen Hui-chuan, Exact solution of Navier-Stokes equation, the otheory of functions of a complex variable under Dirac-Pauli representation and its application in fluid dynamics (II),Appl. Math. Mech. 7, 6 (1986).
Prandtl, L., K. Oswatitsch and K. Wieghardt,Führer Durch die Strömungslehre, Friedr. Vieweg + Sohn, Braunschweig (1969).
Fung, Y. C.,A First Course in Continuum Mechanics, ((2nd ed.) Prentice-Hall, Inc. (1977).
Hideki, Yukawa,The Basic of Modern Physics, Vol. 1,Classical Physics (I), Iwanami (1975). in Japanese)
Dirac, P. A. M.,The Principle of Quantum Mechanics, Oxford (1958).
Flügge, S.,Practical Quantum Mechanics, Springer-Verlag (1974).
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Communicated by Chien Wei-zang
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Hui-chuan, S. 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). Appl Math Mech 7, 755–766 (1986). https://doi.org/10.1007/BF01900608
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DOI: https://doi.org/10.1007/BF01900608