| 摘要: |
| 本文研究二维Benjamin-Ono-Zakharov-Kuznetsov（BO-ZK）方程的柯西问题. 借助Esfahani等人关于BO-ZK方程相应线性问题的Strichartz估计. 使用半群理论，运用Littlewood-Paley分解技术，使用交换子估计，将方程的非线性项分为不同频率的成分，得到了方程解的高阶估计. 结合能量估计，构造光滑解的序列，在低正则Sobolev空间 H^s(R^2)（s>11/8）中证明了方程解的局部适定性，从而丰富了BO-ZK方程柯西问题的相关结论. |
| 关键词: BO-ZK方程 柯西问题 低正则性解 局部适定性 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| The cauchy problem for the two-dimensional Benjamin-Ono-Zakharov-Kuznetsov equation |
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yangyang1, yanghan2
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1.西南交通大学;2.Southwest Jiaotong University
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| Abstract: |
| This paper studies the Cauchy problem for the two-dimensional Benjamin-Ono-Zakharov-Kuznetsov (BO-ZK) equation. With the help of the Strichartz estimates established by Esfahani et al. for the corresponding linear problem of the BO-ZK equation, we employ semigroup theory, Littlewood-Paley decomposition techniques, and commutator estimates to decompose the nonlinear term of the equation into components of different frequencies, thereby obtaining higher-order estimates for the solutions. Combining energy estimates, we construct a sequence of smooth solutions and prove the local well-posedness of the equation in low-regularity Sobolev spaces H^s(R^2) (s > 11/8) . This work enriches the existing conclusions related to the Cauchy problem of the BO-ZK equation. |
| Key words: BO-ZK equation Cauchy problem Low regularity solutions local well-posedness |
