# Solutions of Magnetohydrodynamics equations—The theory of functions of a complex variable under Dirac-pauli representation and its application in fluid dynamics (IV)

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## Abstract

- (A)
We turn the Magnetohydrodynamics equaitons of isentropic compressible and non-dissipative magneto-flow into the form of the ideal hydrodynamics equations in this paper; we can obtain the general Chaplygin equation from Ref. [3], and the general sduction of this equation.

- (B)
We apply the theory of functions of a complex rariable under Dirac-pauli representation, turn the general Magnetohydrodynamics equations of incompressible mageto-flow into two nonlinear equaitons for flow function and “magneto-flow function”, and obtain the exact stable solution of incompressible magnetohydrodynamics equations under the condition of stable magnetic field (i.e. under conditon of equality for kinematical viscid coefficient or viscid diffusion coefficient with magnetic diffusion coefficient).

## Keywords

Magnetic Field Mathematical Modeling Diffusion Coefficient Fluid Dynamic Industrial Mathematic## Preview

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