Communications in Mathematical Sciences

Volume 17 (2019)

Number 3

Sharp energy criteria and singularity of blow-up solutions for the Davey–Stewartson system

Pages: 653 – 667



Jian Zhang (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, China)

Shihui Zhu (School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan, China)


By analyzing the geometric characteristic of related algebra equations, we first find the sharp energy criteria of singular solutions and global solutions for the Davey–Stewartson systems. Then, we study the limiting behavior of singular solutions, and obtain the rate of convergence of singular solutions, rate of concentration of singular solutions for Davey–Stewartson systems with the $L^2$ super-critical nonlinearity.


Davey–Stewartson system, singular solution, sharp energy criteria, concentration

2010 Mathematics Subject Classification

35Q55, 45G05

This paper was supported by the National Natural Science Foundation of China grant No. 11771314 and No. 11871138, and by the Excellent Youth Foundation of Sichuan Scientific Committee, grant No. 2014JQ0039.

Received 13 April 2018

Accepted 22 January 2019

Published 30 August 2019