Energy criterion of global existence for energy-critical Schrödinger equations with subcritical perturbations

Abstract

We present a variational approach to study the energy-critical Schrödinger equations with subcritical perturbations. Through analysing the Hamiltonian property we establish two types of invariant evolution flows, and derive a new sharp energy criterion for blowup of solutions for the equation. Furthermore, we answer the question: how small are the initial data such that the solutions of this equation are bounded in H ¹(R ^N )?

Keywords:

• energy criterion
• energy-critical Schrödinger equations
• subcritical perturbations
• global existence
• blowup

AMS Subject Classifications:

• 35Q55
• 35A15
• 35B30

Acknowledgements

The project is supported by the National Science Foundation of China (Grant no. 10771151 and no. 10726033), the Scientific Research Found of Sichuan Provincial Education Department (Grant no. 2006A063) and the Scientific Research Found of Science and Technology Bureau of Sichuan Province (Grant no. 07JY029-012).