一类6阶晶格振动方程局部解的存在性

The Local Existence of a Sixth Order Lattice Dynamics Equation

研究了一类弹性晶体的晶格振动问题,利用Fourier变换把问题转化为与之等价的积分方程.根据KdV方程的Strichartz估计和关于容许对的2个引理,构造了一类辅助空间.对不同的非线性项,相应地改变初值的正则性指标范围,利用压缩映射原理,证明了晶格振动方程Cauchy问题局部解的存在性定理.

We study a sixth order lattice dynamics equation. Firstly, we transfer the equation into an integral equation by Fourier transform. Using the Strichartz estimates of the KdV equation and two lemmas of the admissible pairs, we construct some auxiliary spaces. On some assumption on the nonlinearity and the regularity index, the local existence results are proved by the contraction mapping theorem.