%A Xiao Su,Shubin Wang %T The Cauchy Problem for the Forth Order p-Generalized Benney-Luke Equation %0 Journal Article %D 2022 %J Acta mathematica scientia,Series A %R %P 1744-1753 %V 42 %N 6 %U {http://121.43.60.238/sxwlxbA/CN/abstract/article_16889.shtml} %8 2022-12-26 %X

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.