Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1744-1753.

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The Cauchy Problem for the Forth Order p-Generalized Benney-Luke Equation

Xiao Su1,*(),Shubin Wang2()   

  1. 1 College of Science, Henan University of Technology, Zhengzhou 450001
    2 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001
  • Received:2021-10-26 Online:2022-12-26 Published:2022-12-16
  • Contact: Xiao Su;
  • Supported by:
    the Natural Science Foundation of Henan(202300410109);the Fundamental Research Funds for the Henan Provincial Colleges and Universities in Henan University of Technology(2018QNJH19);the training plan for young backbone teachers of Henan University of Technology


We consider the global existence and uniqueness of the Cauchy problem for the forth order $p$-generalized Benney Luke equatoion in the natural energy space $\dot{H}^{1}(\mathbb{R}^n)\cap\dot{H}^{2}(\mathbb{R}^n) \times H^1(\mathbb{R}^n)$. First of all, the local existence and uniqueness of solutions are investigated in the energy space by means of the contraction mapping principle. Secondly, in the case of source nonlinearity, we provide the sufficient conditions of the existence of global solutions.

Key words: $p$-generalized Benney-Luke equation, Cauchy problem, Global solutions

CLC Number: 

  • O175.29