Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations

Shanshan Yang; Hongbiao Jiang; Yinhe Lin

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 4, page 1189-1198
  • ISSN: 0011-4642

Abstract

top
We study compressible isentropic Navier-Stokes-Poisson equations in ℝ 3 . With some appropriate assumptions on the density, velocity and potential, we show that the classical solution of the Cauchy problem for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing will blow up in finite time. The proof is based on a contradiction argument, which relies on proving the conservation of total mass and total momentum.

How to cite

top

Yang, Shanshan, Jiang, Hongbiao, and Lin, Yinhe. "Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations." Czechoslovak Mathematical Journal 71.4 (2021): 1189-1198. <http://eudml.org/doc/297886>.

@article{Yang2021,
abstract = {We study compressible isentropic Navier-Stokes-Poisson equations in $\{\mathbb \{R\}\}^3$. With some appropriate assumptions on the density, velocity and potential, we show that the classical solution of the Cauchy problem for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing will blow up in finite time. The proof is based on a contradiction argument, which relies on proving the conservation of total mass and total momentum.},
author = {Yang, Shanshan, Jiang, Hongbiao, Lin, Yinhe},
journal = {Czechoslovak Mathematical Journal},
keywords = {compressible isentropic Navier-Stokes-Poisson equation; unipolar; energy solution; blow-up},
language = {eng},
number = {4},
pages = {1189-1198},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations},
url = {http://eudml.org/doc/297886},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Yang, Shanshan
AU - Jiang, Hongbiao
AU - Lin, Yinhe
TI - Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 1189
EP - 1198
AB - We study compressible isentropic Navier-Stokes-Poisson equations in ${\mathbb {R}}^3$. With some appropriate assumptions on the density, velocity and potential, we show that the classical solution of the Cauchy problem for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing will blow up in finite time. The proof is based on a contradiction argument, which relies on proving the conservation of total mass and total momentum.
LA - eng
KW - compressible isentropic Navier-Stokes-Poisson equation; unipolar; energy solution; blow-up
UR - http://eudml.org/doc/297886
ER -

References

top
  1. Cho, Y., Jin, B. J., 10.1016/j.jmaa.2005.08.005, J. Math. Anal. Appl. 320 (2006), 819-826. (2006) Zbl1121.35110MR2225997DOI10.1016/j.jmaa.2005.08.005
  2. Dong, J., Ju, Q., 10.1360/N012018-00134, Sci. Sin., Math. 50 (2020), 873-884 Chinese. (2020) DOI10.1360/N012018-00134
  3. Dong, J., Zhu, J., Wang, Y., 10.21136/CMJ.2019.0156-18, Czech. Math. J. 70 (2020), 9-19. (2020) Zbl07217119MR4078344DOI10.21136/CMJ.2019.0156-18
  4. Gamba, I. M., Gualdani, M. P., Zhang, P., 10.1007/s00605-009-0092-4, Monatsh Math. 157 (2009), 37-54. (2009) Zbl1173.35106MR2504777DOI10.1007/s00605-009-0092-4
  5. Guo, B., Wang, G., 10.1016/j.jde.2016.06.007, J. Differ. Equations 261 (2016), 3815-3842. (2016) Zbl1354.35123MR3532056DOI10.1016/j.jde.2016.06.007
  6. Guo, B., Wang, G., 10.1063/1.4978331, J. Math. Phys. 58 (2017), Article ID 031505, 11 pages. (2017) Zbl1359.76348MR3626024DOI10.1063/1.4978331
  7. Jiu, Q., Wang, Y., Xin, Z., 10.1016/j.jde.2015.04.007, J. Differ. Equations 259 (2015), 2981-3003. (2015) Zbl1319.35194MR3360663DOI10.1016/j.jde.2015.04.007
  8. Lai, N.-A., 10.1016/j.nonrwa.2015.03.005, Nonlinear Anal., Real World Appl. 25 (2015), 112-117. (2015) Zbl1327.35299MR3351014DOI10.1016/j.nonrwa.2015.03.005
  9. Lei, Z., Du, Y., Zhang, Q., 10.4310/MRL.2013.v20.n1.a4, Math. Res. Lett. 20 (2013), 41-50. (2013) Zbl1284.35329MR3126720DOI10.4310/MRL.2013.v20.n1.a4
  10. Rozanova, O., 10.1016/j.jde.2008.07.007, J. Differ. Equations 245 (2008), 1762-1774. (2008) Zbl1154.35070MR2433485DOI10.1016/j.jde.2008.07.007
  11. Wang, G., Guo, B., Fang, S., 10.1002/mma.4384, Math. Methods Appl. Sci. 40 (2017), 5262-5272. (2017) Zbl1383.35034MR3689262DOI10.1002/mma.4384
  12. Xin, Z., 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C, Commun. Pure Appl. Math. 51 (1998), 229-240. (1998) Zbl0937.35134MR1488513DOI10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C
  13. Xin, Z., Yan, W., 10.1007/s00220-012-1610-0, Commun. Math. Phys. 321 (2013), 529-541. (2013) Zbl1287.35059MR3063918DOI10.1007/s00220-012-1610-0

NotesEmbed ?

top

You must be logged in to post comments.