TY - JOUR
T1 - The Cauchy Problem for the Sixth Order $p$-Generalized Benney-Luke Equation
AU - Su , Xiao
AU - Li , Xiao
AU - Wang , Shubin
JO - Journal of Mathematical Study
VL - 2
SP - 133
EP - 148
PY - 2024
DA - 2024/06
SN - 57
DO - http://doi.org/10.4208/jms.v57n2.24.01
UR - https://global-sci.org/intro/article_detail/jms/23165.html
KW - $p$-generalized Benney-Luke equation, Cauchy problem, Global existence.
AB - <p style="text-align: justify;">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.</p>