Sharp criteria of blow-up for the energy-critical nonlinear wave equation with a damping term

Abstract

In terms of the best constant of the critical Sobolev inequality, by establishing two invariant flows, we find the sharp criteria of blow-up and global existence of solutions for the energy-critical nonlinear wave equation with a damping term.

Keywords:

• Nonlinear wave equation
• energy-critical
• criteria
• blow-up

2010 Mathematical Subject Classifications:

• 35Q40
• 35L05

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11371267], and the 12th Five-Year Plan of Education and Scientific Research in Guangdong Provence, China [grant number 2013JK247].