Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up t...Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.展开更多
By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three_dimensional square cell pattern of Rayleigh_Benard convection. The result means tha...By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three_dimensional square cell pattern of Rayleigh_Benard convection. The result means that our method enables this three_dimensional flow pattern to be described in an unambiguous manner, and some experimental results of other authors can be explained.展开更多
基金Supported by the Natural Science Foundation of Henan Province(092300410150)the Key Youth Teacher Foundation of Department Education of Henan Province(2011GGJS-210)the Key Youth Teacher Foundation of Huanghuai University
文摘Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.
文摘By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three_dimensional square cell pattern of Rayleigh_Benard convection. The result means that our method enables this three_dimensional flow pattern to be described in an unambiguous manner, and some experimental results of other authors can be explained.
