ON PROBLEMS IN THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY AND ITS IMPROVEMENT

<正> There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra-dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimationfor it.(2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed bymany practical problems.(3) When the linear part of its solution does not correspond to a neutral case. thereare more than one way in determining the Landau constants, and practically no one knows which is the bestway. In this paper, problems(1)and(2)are solved theoretically, and ways for its improvement have been proposed.By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clari-fied.