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

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

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.

Author Details

Xiao Su

Xiao Li

Shubin Wang