二维Benjamin-Ono-Zakharov-Kuznetsov方程的规范解  

Normalized Solitary Waves of the Two-Dimensional Generalized Benjamin-Ono-Zakharov-Kuznetsov Equation

作　　者：王元舜 

机构地区：[1]上海理工大学理学院,上海

出　　处：《理论数学》2023年第4期1122-1134,共13页Pure Mathematics

摘　　要：利用集中紧性原理、极大极小值方法和Gagliardo-Nirenberg不等式,研究了在L2-次临界和L2-临界的情况下,二维Benjamin-Ono-Zakharov-Kuznetsov (BO-ZK)方程的规范解的存在性和稳定性问题。首先通过限制,证明能量泛函H(Q)极小值的存在性,然后证明其稳定性,最终证明了在L2-次临界下泛函Sa(Q)可以取到最小值,从而证明存在基态解。本文所得到的结论,即证明BO-ZK方程解的存在性和稳定性,在物理学领域中有着广泛的应用。The existence and stability of the solution for normalized solitary waves of the two-dimensional generalized Benjamin-Ono-Zakharov-Kuznetsov Equation were studied by using concentration compactness principle, minimax theory and Gagliardo-Nirenberg in equality in the L2-subcritical case and the L2-critical case. Firstly, the existence of minimum to the energy functional under the condition of , then the stability is verified. Thus, it is proved that the minimum value of functional Sa(Q) can be obtained in the L2-subcritical case and there exist ground state solutions. The conclusion of this article, that the existence and stability of the solution of BO-ZK equation, is widely applied in physics.

关 键 词：BO-ZK方程 基态解 存在性 稳定性 集中紧性原理 

分 类 号：G63[文化科学—教育学]