【摘要】 利用速度场u的Poloidal-Toroidal分解,把描述Bénard系统的偏微分方程组Boussinesq方程组转化为一个等价的方程组。当本征值σ=0时,将其线性化问题转化为一个常微分方程组,然后选择适当的Hilbert空间对方程组中的算子进行研究,并证明它们都是严格正定的自共轭的线性算子,进而得出该系统稳定性研究中一些本征值问题的解的性质。更多还原

【Abstract】 The partial differential equation describing the Bénard system is the Boussinesq equation.It is shown that the Boussesq equation can be transformed into an equivalent one by applying the Poloidal-Torodial decomposition of a velocity field u.After choosing an appropriate Hilbert space,it can be shown that these operators are strictly positive,definite and self-conjugate,and that when the eigenvalue σ=0,some properties of the solution for the stability analysis of the Bénard system can be obtained.更多还原