A global existence and blow-up threshold for Davey-Stewartson equations in $\mathbb{R}^3$
A global existence and blow-up threshold for Davey-Stewartson equations in $\mathbb{R}^3$
In this paper we study the threshold of global existenceand blow-up for the solutions to the generalized 3DDavey-Stewartson equations\begin{equation*} \left\{ \begin{aligned} & iu_t + \Delta u + |u|^{p-1} u + E_1(|u|^2)u = 0, \quad t > 0, \ \ x\in \mathbb{R}^3, \\ & u(0,x) = u_0(x) \in H^1(\mathbb{R}^3), \end{aligned} \right.\end{equation*}where …