Blowup for C¹ solutions of compressible Euler equations with time-dependent damping

Jianli LIU, Jingjie WANG, Man Wai YUEN

Research output: Contribution to journalArticlespeer-review

Abstract

In this paper, we will show the blowup phenomenon of solutions to the compressible Euler equations with time-dependent damping. Firstly, under the assumptions that the radially symmetric initial data and initial density contains vacuum states, the singularity of the classical solutions will formed in finite time in Rⁿ(n≥2). Furthermore, we can also find a sufficient condition for the functional of initial data such that smooth solution of the irrotational compressible Euler equations with time-dependent damping breaks down in finite time for all kinds of fractional coefficients in Rⁿ(n≥2). Copyright © 2021 by International Press of Boston, Inc. All rights reserved.
Original languageEnglish
Pages (from-to)513-528
JournalCommunications in Mathematical Sciences
Volume19
Issue number2
DOIs
Publication statusPublished - 2021

Citation

Liu, J., Wang, J., & Yuen, M. (2021). Blowup for C¹ solutions of compressible Euler equations with time-dependent damping. Communications in Mathematical Sciences, 19(2), 513-528. doi: 10.4310/CMS.2021.v19.n2.a9

Keywords

  • Euler equations
  • Singularity formation
  • Time-dependent damping
  • Vacuum

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