Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 8
125
Views
3
CrossRef citations to date
0
Altmetric
Articles

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

&
Pages 1774-1785 | Received 23 May 2019, Accepted 14 Aug 2019, Published online: 30 Aug 2019

References

  • Lions PL. Mathematical topics in fluid mechanics. Vol. 1. Oxford: Clarendon Press; 1996.
  • Lions PL. Mathematical topics in fluid mechanics. Vol. 2. Oxford: Clarendon Press; 1998.
  • Sideris TC. Formation of singularities in three-dimensional compressible fluids. Comm Math Phys. 1985;101:475–485. doi: 10.1007/BF01210741
  • Sideris TC. Formation of singularities in solutions to nonlinear hyperbolic equations. Arch Ration Mech Anal. 1984;86:369–381. doi: 10.1007/BF00280033
  • Cheung KL. Blowup phenomena for the N-dimensional compressible euler equations with damping. Z Angew Math Phys. 2017;68:1–8. doi: 10.1007/s00033-016-0745-9
  • Cheung KL. Blowup of solutions for the initial boundary value problem of the 3–dimensional compressible damped euler equations. Math Method Appl Sci. 2018;41:4754–4762. doi: 10.1002/mma.4928
  • Yuen MW. Blowup for irrotational C1 solutions of the compressible euler equations in RN. Nonlinear Anal. 2017;158:132–141. doi: 10.1016/j.na.2017.04.007
  • Zhu X, Tu A. Blowup of the axis-symmetric solutions for the IBVP of the isentropic euler equations. Nonlinear Anal. 2014;95:99–106. doi: 10.1016/j.na.2013.08.022
  • Sideris TC, Thomases B, Wang DH. Long time behavior of solutions to the 3D compressible euler equations with damping. Commun Partial Differ Equ. 2003;28:795–816. doi: 10.1081/PDE-120020497
  • Pan X. Blow up of solutions to 1d-Euler equations with time-dependent damping. J Math Anal Appl. 2016;442:435–445. doi: 10.1016/j.jmaa.2016.04.075
  • Pan X. Global existence of solutions to 1-d euler equations with time-dependent damping. Nonlinear Anal. 2016;132:327–336. doi: 10.1016/j.na.2015.11.022
  • Hou F, Yin H. On the global existence and blowup of smooth solutions to the multi-dimensional compressible euler equations with time-depending damping. Nonlinearity. 2017;30:2485–2517. doi: 10.1088/1361-6544/aa6d93

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.