Abstract: In this paper:(A)We cast aside the traditional quaternion theory and build up the theory of functions of a complex variable under Dirac-Pauli representation.Thus the multivariate and multidimensional problems become rather simple problems.(B)We simplify the Navier-Stokes equation of incompressible viscous fluid dynamics and the equations group ofisentropic aerodynamics by theory of functions of a complex variable under Dirac-Pauli representation.And the above-equations,as central problems of fluid dynamics,are classified as the nonlinear equation with only one complex unknown function.