On finite-time blowup mechanism of irrotational compressible Euler equations with time-dependent damping

ABSTRACT

In this paper, sufficient initial conditions for finite-time blowup of smooth solutions of the irrotational compressible Euler equations with time-dependent damping are established. Our blowup conditions reveal that for sufficiently large initial velocity, fixed background density and with no largeness assumption on the initial density, the velocity of the fluid must collapse in finite time on some subset of general Euclidean space with non-zero Lebesgue measure.

Keywords:

• Blowup
• time-dependent damping
• compressible Euler equations
• exponential growth
• irrotational fluids

2010 Mathematics Subject Classifications:

• 35B44
• 35L67
• 35Q31
• 35B30

Acknowledgments

The authors would like to thank the reviewers for useful comments and suggestions for the improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research is partially supported by the 2019-20 Departmental Collaborative Research Fund and 2019-20 SRG of the Department of Mathematics and Information Technology, The Education University of Hong Kong. 2019-20 Departmental Collaborative Research Fund,2019-20 SRG of the Department of Mathematics and I