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
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。
Abstract: 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.
文章引用：王元舜. 二维Benjamin-Ono-Zakharov-Kuznetsov方程的规范解[J]. 理论数学, 2023, 13(4): 1122-1134. https://doi.org/10.12677/PM.2023.134117

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