五次长短波共振方程初值问题解的存在性

Existence of Solutions for the Initial Value Problems of a Five-Time Long-Short Wave Resonance Equation

研究了五次长短波共振方程初值问题解的存在性。首先利用压缩映射原理证明了局部解的存在性,然后通过建立局部解具能量守恒性质,并利用先验估计方法,证明了具有高次非线性项的长短波共振方程的局部解可以延拓到整个定义域,最终证明了全局解的存在性。

The existence of the solutions to the initial value problem of a five-time long-short wave resonance equation was focused.First,the existence of the local solution was proved by using the compression mapping theorem.Then,the local solution with energy conservation properties was established and the prior estimation method was used to,It was also proved that the local solution of high-order nonlinear terms in the five-time long-short wave resonance equation can be extended to the whole domain.Finally,the existence of the global solution was testified.