In this paper, the initial-boundary value problem of the multidimensional compressible Euler equations with time-dependent damping in radial symmetry is considered. It is shown that finite-time singularity will be developed for the C¹ solutions of the compressible Euler equations with time-dependent damping coefficients μ/((1+t)λ), μ > 0, λ ≥ 0 if the initial value of a newly introduced functional, F(t) = ∫1∞ ρ(t,r)u(t,r) [rN − α(t)] dr with a time-dependent parameter α(t) is sufficiently large. The blowup conditions imply that the initial kinetic energy of the fluid must not be less than a given constant. Copyright © 2019 Informa UK Limited, trading as Taylor & Francis Group.
CitationCheung, K. L., & Wong, S. (2019). Finite-time singularity formation for C¹ solutions to the compressible Euler equations with time-dependent damping. Applicable Analysis. Advance online publication. doi: 10.1080/00036811.2019.1659961
- Time-dependent damping
- Euler equations
- Initial-boundary value problem
- Differential inequality