Abstract: The dissipative equilibrium dynamics studied the law of fluid motion under constraints in the contact in terface of the coupling system. It needed to examine how constraints actupon the fluid movement, while the fluid movement reacted to the constraint field. It also needed to examine the coupling fluid field and media with in the contact in terface, and to use the multi-scale analys is to solve the regular and singular perturbation problems in micro-phenomen a of laboratories and macro-phenomena of nature. The field affected by the gravity constraints was described. A pplying the multi-scale analysis to the complex Fourier harmonic analysis, scale changes, and the in troduction of new parameters, the complex threed miensional coupling dynamic equations were trans formed in to a boundary layer problem in the one-dimensional complex space. Asymptotic analys is was carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples were given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further an alysis and calculation on non-lineare igenfunctions of the contact in terface dynamic problems by the eigenvalue relation, anasymptotic perturbation solution was obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact in terface was obtained by asymptotic estmiates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact in terface.