The Cauchy Problem for the Sixth Order $p$-Generalized Benney-Luke Equation (Journal of Mathematical Study, 2024)
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 andprovide the sufficient conditions of the global existence of solutions by analyzing theproperties of the energy functional.