Abstract: This article described the complex fluid and the field constraints with gravitational effects.The asymptotic solution determines the dissipative equilibrium vector field of the coupled convection disturbance kinetic equations. For the analysis of the canonical and singular perturbation problems we analyze the micro-phenomena of the laboratory and macro-phenomena of nature.Our approach is to use the complex Fourier harmonic analysis, re-scale, and the introduction of new parameters to reduce the three-dimensional coupling dynamic equations into a one-dimensional complex space of boundary-layer. Two examples for the problem of the perturbation characteristic function were given with asymptotic analysis. Example 2 explains the turning point of the transition that from the index oscillation solution to the algebraic solution.

Key words: boundary problem, asymptotic perturbation analysis, turning point, coupling dynamics equations, boundary problem, asymptotic perturbation analysis, turning point