Year: 2024
Author: Xiao Su, Xiao Li, Shubin Wang
Journal of Mathematical Study, Vol. 57 (2024), Iss. 2 : pp. 133–148
Abstract
We investigate the Cauchy problem for the sixth order $p$-generalized Benney-Luke equation. The local well-posedness is established in the energy space $\dot{H}^1 (\mathbb{R}^n)∩ \dot{H}^3(\mathbb{R}^n)$ for $1 ≤ n ≤ 10,$ by means of the Sobolev multiplication law and the contraction mapping principle. Moreover, we establish the energy identity of solutions and provide the sufficient conditions of the global existence of solutions by analyzing the properties of the energy functional.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v57n2.24.01
Journal of Mathematical Study, Vol. 57 (2024), Iss. 2 : pp. 133–148
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: $p$-generalized Benney-Luke equation Cauchy problem Global existence.