Sharp threshold for scattering of a generalized Davey-Stewartson system in three dimension

Jing  Lu; Yifei  Wu

doi:10.3934/cpaa.2015.14.1641

Article Contents

2015, Volume 14, Issue 5: 1641-1670. Doi: 10.3934/cpaa.2015.14.1641

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Sharp threshold for scattering of a generalized Davey-Stewartson system in three dimension

Jing Lu^1, and
Yifei Wu^2,

1.
China Academy of Engineering Physics, Beijing 100088
2.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 1000875

Received: October 31, 2013

Revised: November 30, 2014

Published: August 2015

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Abstract

In this paper, we consider the Cauchy problem for the generalized Davey-Stewartson system \begin{eqnarray} &i\partial_t u + \Delta u =-a|u|^{p-1}u+b_1uv_{x_1}, (t,x)\in R \times R^3,\\ &-\Delta v=b_2(|u|^2)_{x_1}, \end{eqnarray} where $a>0,b_1b_2>0$, $\frac{4}{3}+1< p< 5$. We first use a variational approach to give a dichotomy of blow-up and scattering for the solution of mass supercritical equation with the initial data satisfying $J(u_0)

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Mathematics Subject Classification: Primary 35Q53; Secondary 47J35.

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