The Cauchy Problem for Higher-Order KdV Equations Forced by White Noise

摘要：

主要研究受白噪声驱动的高阶KdV型方程的Cauchy问题.通过在某些Bourgain空间中建立双线性估计、三线性估计,并利用Ito公式、BDG不等式和停时技巧,建立相应的局部适定性和整体适定性.这些技巧可以用以研究其他具有哈密顿结构的方程的局部适定性和整体适定性.

The present paper is devoted to the study on the Cauchy problem for the higher-order KdV type equations forced by white noises. By establishing bilinear and trilinear estimates in some Bourgain spaces, we prove the local well-posedn-ess and global well-posedness of corresponding problems. The key ingredients that we used are bilinear/trilinear estimates, Ito formula and the BDG inequality as well as the stopping time technique. Furthermore, the techniques used in this paper can be applied to study the local well-posedness and global well-posedness of other dispersive equations with Hamiltonian structure.

作者：

李用声 闫威

Li Yongsheng Yan Wei(School of Mathematics, South China University of Technology,Guangzhou 510640, China School of Mathematics and Information Science, Henan Normal University？Xinxiang 453007,China)

机构地区：

华南理工大学数学学院 betway官方app 数学与信息科学学院

出处：

《betway官方app 学报：自然科学版》 CAS 北大核心 2017年第4期1-9,共9页

基金：

国家自然科学基金(11571118 11401180)

关键词：

CAUCHY问题 白噪声驱动的高阶KdV型方程 ITO公式 BDG不等式 停时技巧

Cauchy problem Higher-order KdV type equation white noise Ito formula BDG inequality Stopping time technique

分类号：

O175.29 [理学—基础数学]

白噪声驱动的高阶KdV型方程的Cauchy问题.pdf