Title:
|
Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations (English) |
Author:
|
Yang, Shanshan |
Author:
|
Jiang, Hongbiao |
Author:
|
Lin, Yinhe |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
71 |
Issue:
|
4 |
Year:
|
2021 |
Pages:
|
1189-1198 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
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. (English) |
Keyword:
|
compressible isentropic Navier-Stokes-Poisson equation |
Keyword:
|
unipolar |
Keyword:
|
energy solution |
Keyword:
|
blow-up |
MSC:
|
35B44 |
MSC:
|
35Q35 |
idZBL:
|
Zbl 07442484 |
idMR:
|
MR4339121 |
DOI:
|
10.21136/CMJ.2021.0347-20 |
. |
Date available:
|
2021-11-08T16:06:08Z |
Last updated:
|
2024-01-01 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149248 |
. |
Reference:
|
[1] Cho, Y., Jin, B. J.: Blow-up of viscous heat-conducting compressible flows.J. Math. Anal. Appl. 320 (2006), 819-826. Zbl 1121.35110, MR 2225997, 10.1016/j.jmaa.2005.08.005 |
Reference:
|
[2] Dong, J., Ju, Q.: Blow-up of smooth solutions to compressible quantum Navier-Stokes equations.Sci. Sin., Math. 50 (2020), 873-884 Chinese. 10.1360/N012018-00134 |
Reference:
|
[3] Dong, J., Zhu, J., Wang, Y.: Blow-up for the compressible isentropic Navier-Stokes-Poisson equations.Czech. Math. J. 70 (2020), 9-19. Zbl 07217119, MR 4078344, 10.21136/CMJ.2019.0156-18 |
Reference:
|
[4] Gamba, I. M., Gualdani, M. P., Zhang, P.: On the blowing up of solutions to quantum hydrodynamic models on bounded domains.Monatsh Math. 157 (2009), 37-54. Zbl 1173.35106, MR 2504777, 10.1007/s00605-009-0092-4 |
Reference:
|
[5] Guo, B., Wang, G.: Blow-up of the smooth solution to quantum hydrodynamic models in $\mathbb R^d$.J. Differ. Equations 261 (2016), 3815-3842. Zbl 1354.35123, MR 3532056, 10.1016/j.jde.2016.06.007 |
Reference:
|
[6] Guo, B., Wang, G.: Blow-up of solutions to quantum hydrodynamic models in half space.J. Math. Phys. 58 (2017), Article ID 031505, 11 pages. Zbl 1359.76348, MR 3626024, 10.1063/1.4978331 |
Reference:
|
[7] Jiu, Q., Wang, Y., Xin, Z.: Remarks on blow-up of smooth solutions to the compressible fluid with constant and degenerate viscosities.J. Differ. Equations 259 (2015), 2981-3003. Zbl 1319.35194, MR 3360663, 10.1016/j.jde.2015.04.007 |
Reference:
|
[8] Lai, N.-A.: Blow up of classical solutions to the isentropic compressible Navier-Stokes equations.Nonlinear Anal., Real World Appl. 25 (2015), 112-117. Zbl 1327.35299, MR 3351014, 10.1016/j.nonrwa.2015.03.005 |
Reference:
|
[9] Lei, Z., Du, Y., Zhang, Q.: Singularities of solutions to compressible Euler equations with vacuum.Math. Res. Lett. 20 (2013), 41-50. Zbl 1284.35329, MR 3126720, 10.4310/MRL.2013.v20.n1.a4 |
Reference:
|
[10] Rozanova, O.: Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations.J. Differ. Equations 245 (2008), 1762-1774. Zbl 1154.35070, MR 2433485, 10.1016/j.jde.2008.07.007 |
Reference:
|
[11] Wang, G., Guo, B., Fang, S.: Blow-up of the smooth solutions to the compressible Navier-Stokes equations.Math. Methods Appl. Sci. 40 (2017), 5262-5272. Zbl 1383.35034, MR 3689262, 10.1002/mma.4384 |
Reference:
|
[12] Xin, Z.: Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density.Commun. Pure Appl. Math. 51 (1998), 229-240. Zbl 0937.35134, MR 1488513, 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C |
Reference:
|
[13] Xin, Z., Yan, W.: On blowup of classical solutions to the compressible Navier-Stokes equations.Commun. Math. Phys. 321 (2013), 529-541. Zbl 1287.35059, MR 3063918, 10.1007/s00220-012-1610-0 |
. |