Finite-time singularity formation for C¹ solutions to the compressible Euler equations with time-dependent damping

Ka Luen CHEUNG, Sen WONG

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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) [r− 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.
Original languageEnglish
JournalApplicable Analysis
Early online dateAug 2019
DOIs
Publication statusE-pub ahead of print - Aug 2019

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Finite-time Singularities
Compressible Euler Equations
Euler equations
Damping
Kinetic energy
Boundary value problems
Radial Symmetry
Initial-boundary-value Problem
Blow-up
Fluids
Imply
Fluid
Coefficient

Citation

Cheung, 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

Keywords

  • Blowup
  • Time-dependent damping
  • Euler equations
  • Initial-boundary value problem
  • Differential inequality