为了研究等离子体物理中Zakharov方程组数值方法解的适定性,本文针对Zakharov方程组的周期初值问题,首先在[0,T]上建立了半离散的Fourier谱格式;然后,证明了半离散Fourier谱格式具有守恒性质;最后,利用守恒性质对方程组的近似解进行先验估计,得到了整体解的存在性。

In order to study well-posed problem of the numerical solutions method for Zakharov equations in plasma physics, first, according to the periodic initial value problem of the equations, a semi-discrete Fourier spectral scheme is constructed in the closed region of [0, T]. Second, the conservative property of the semi-discrete spectral scheme is proved. And at last, the conservative property is used to obtain the priori estimate of approximate solution and the existence of global solution for Zakharov equations.