Communications in Mathematical Sciences
Volume 17 (2019)
Sharp energy criteria and singularity of blow-up solutions for the Davey–Stewartson system
Pages: 653 – 667
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
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