The lifespan of classical solutions to the (damped) compressible Euler equations


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In this paper, the initial-boundary value problem of the original three-dimensional compressible Euler equations with (or without) time-dependent damping is considered. By considering a functional F(t,α,f) weighted by a general time-dependent parameter function α and a general radius-dependent parameter function f, we show that if the initial value F|t=0 is sufficiently large, then the lifespan of the system is finite. Here, f can be any C¹ strictly increasing function such that the sum of initial values of f and α is non-negative. It follows that a class of conditions for non-existence of global classical solutions is established. Moreover, the conditions imply that a strong α will lead to a more unrestrained necessary condition for classical solutions of the system to exist globally in time. Copyright © 2020 Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.
Original languageEnglish
Pages (from-to)1867-1879
JournalBulletin of the Malaysian Mathematical Sciences Society
Issue number4
Early online date17 Oct 2020
Publication statusPublished - Jul 2021


Cheung, K. L., & Wong, S. (2021). The lifespan of classical solutions to the (damped) compressible Euler equations. Bulletin of the Malaysian Mathematical Sciences Society, 44(4), 1867-1879. doi: 10.1007/s40840-020-01036-0


  • Blowup
  • Time-dependent damping
  • Compressible Euler equations
  • Global existence
  • Smooth solutions
  • Lifespan


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