二维广义Camassa-Holm-Kadomtsev-Petviashvili(CH-KP)方程的局部适定性  

The local well-posedness of the two dimensional generalized Camassa-Holm-Kadomtsev-Petviashvili equation

作　　者：王佳敏 可雪丽 臧爱彬[3] WANG Jiamin;KE Xueli;ZANG Aibin(Department of Mathematics, Northwest University, Xi′an 710127, China;School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China;Center of Applied Mathematics, School of Mathematics and Computer Science, Yichun University, Yichun 336000, China)

机构地区：[1]西北大学数学学院,陕西西安710127 [2]湘潭大学数学与计算科学学院,湖南湘潭411105 [3]宜春学院数学与计算机科学学院/应用数学研究中心,江西宜春336000

出　　处：《西北大学学报（自然科学版）》2022年第2期298-317,共20页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金(11931013,11771382)。

摘　　要：研究了二维广义Camassa-Holm-Kadomtsev-Petviashvili(CH-KP)方程的柯西问题。通过先验估计、数学连续性归纳法,并结合逼近方法与紧性理论,建立了广义CH-KP方程唯一解的局部适定性。其创新点在于将二维CH-KP方程的研究结果推广到广义CH-KP方程解的局部适定性。进一步研究了广义CH-KP方程解的爆破准则及相关定理。The main research of this paper is the Cauchy problem of the two-dimensional generalized Camassa-Holm-Kadomtsev-Petviashvili(CH-KP)equation.Through a priori estimation,the bootstrap method,a combination of approximation methods and compactness theory,the local well-posedness of the unique solution of the generalized CH-KP equation is established.Its innovative point lies in extending the research results of the two-dimensional CH-KP equation to the local well-posedness of the solution of the generalized CH-KP equation.Furthermore,the blow-up criterion and related theorems of the solution of the generalized CH-KP equation are studied.

关 键 词：CAMASSA-HOLM方程 广义Camassa-Holm-Kadomtsev-Petviashvili方程 局部适定性 

分 类 号：O175.29[理学—数学]