ON PROBLEMS IN THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY AND ITS IMPROVEMENT
流动稳定性弱非线性理论中的问题及其改进

There are three main problems in the weakly nonlinear theory of hydrody-namic stability: (1) The radius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it. (2) The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems. (3) When the linear part of its solution does not correspond to a neutral case, there are more than one way in determining the Landau constants, and actually no one knows which way would yield the best result. In this paper, the problems (1) and (2) are solved theoretically, ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, the problem in (3) has been clarified.