This paper study the Navier-Stoke-Poisson equations for compressible non-Newtonian fluids in one dimensional bounded intervals. The motion of the fluid is driven by the compressible viscous isentropic flow under the self-gravitational and an external force. The local existence and uniqueness of strong solutions was proved based on some compatibility condition. The main condition is that the initial density vacuum is allowed.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 4) |
| DOI | 10.11648/j.sjams.20160404.13 |
| Page(s) | 134-140 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Strong Solutions, Navier-Stokes-Poisson Equations, Non-Newtonian Fluids, Vacuum
| [1] | R. R. Huilgol, Continuum Mechanics of Viscoelastic Liquids. Hindustan Publishing vorporation: Delhi, 1975. |
| [2] | G. Böhme, Non-Newtonian Fluid Mechanics. Applied Mathematics and Mechanics, North-Holland: Amsterdam, 1987 |
| [3] | J. Málek, J. Nečas, M. Rokyta, M. Ružička, Weak and Measure Valued Solutions to Evolutionary PDEs. Chapman and Hall: New York, 1996. |
| [4] | H. Yuan, X. Xu, “Existence and uniqueness of solutions for a class of non-Newtonian fluids with singularit and vacuum”. Journal of Differential Equations, 2008, 245, pp. 2871-2916. |
| [5] | C. Wang, H. Yuan, “Global strong solutions for a class of compressible non-Newtonian fluids wit caccum”. Mathematical Methods in the Applied Sciences, 2011, 34, pp. 397-417. |
| [6] | Y. Song, H. Yuan, Y. Chen, Z. Guo, “Strong solutions for a 1D fluid-particle interaction non-Newtonian model: The bubbling regime”, Journal of Mathematical Physics, 54, 090501 (2013), pp. 1-12. |
| [7] | Y. Song, H. Wang, Y. Chen, Y. Zhang, “The strong solutions for a class of fluid-particle interaction non-Newtonian models”, boundary Value Problems, 2016: 108, pp. 1-17. |
| [8] | D. Hoff, “Global existence for 1D compressible isentropic Navier-Stokes equations with large initial data”, Transactions of the American Mathematical Society, 1987, 303, pp. 169-181. |
| [9] | P. L. Lions, Mathematical topics in fluids mechanics, vol. 2, Oxford Lecture Series in Mathematics and Its Applications, vol. 10, Clarendon Press, Oxford, 1998. |
| [10] | E. Feireisl, A. Novotny, H. Petzeltová, “On the existence of globally defined weak solution to the Navier-Stokes equations”. Journal of Mathematical Fluid Mechanics, 2001, 3, pp. 358-392. |
| [11] | S. Jiang, P. Zhang, “On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations”. Communications in Mathematical Physics, 2001, 215, pp. 559-581. |
| [12] | S. Jiang, P. Zhang, “Axisymmetric solutions of the 3D Navier-Stokes equations for compressible isentropic fluids”, Journal of de Mathématiques Pures et Applquées, 2003, 82, pp. 949-973. |
| [13] | H. Choe, H. Kim, “Strong solutions of the Navier-Stokes equations for isentropic compressible fluids”. Journal of Differential Equations, 2003, 190, pp. 504-523. |
| [14] | Y. Choe, H. Choe, H. Kim, “Unique solvability of the initial boundary value problems for compressible viscous fluids”. Journal de Mathématiques Pures et Applquées, 2004, 83, pp. 243-275. |
| [15] | H. Choe, H. Kim, “Global existence of the radially symmetri solutions of the Navier Stokes equations for isentropic compressible fluids”, Mathematical Methods in the Applied Sciences, 2005, 28, pp. 1-28. |
| [16] | J. Yin, Z. Tan, “Global exitence of strong solutions of Navier Stokes Poisson equations for one-dimensional isentropic compressible fluids”, Chinese Annals of Mathematics, 2008, 29B (4), pp. 441-458. |
| [17] | J. Yin, Z. Tan, “Local existence of the strong solutions for the full Navier Stokes Poisson equations”. Nonliear Analysis, 2009, 71, pp. 2397-2415. |
| [18] | Z. Wu, “Regularity and asymptotic behavior of 1D compressible Navier-Stokes-Poisson equations with free boundary”, Journal of Mathematical Analysis and Applications, 2011, 374, pp. 29-48. |
| [19] | J. Liu, R. Lian, M. Qian, “Global existence of solutiosn to bipolar Navier-Stokes-Poisson system”, Acta Mathematica Scientia, 2014, 34A (4), pp. 960-976. |
| [20] | R. Duan, S. Liu, “Stability of rarefaction waves of the Navier-stokes-Poisson system”, Journal of Differential Equations, 258, (2015), no. 7, pp. 2495-2530. |
APA Style
Yukun Song, Yang Chen. (2016). Strong Solutions of Navier-Stokes-Poisson Equations for Compressible Non-Newtonian Fluids. Science Journal of Applied Mathematics and Statistics, 4(4), 134-140. https://doi.org/10.11648/j.sjams.20160404.13
ACS Style
Yukun Song; Yang Chen. Strong Solutions of Navier-Stokes-Poisson Equations for Compressible Non-Newtonian Fluids. Sci. J. Appl. Math. Stat. 2016, 4(4), 134-140. doi: 10.11648/j.sjams.20160404.13
AMA Style
Yukun Song, Yang Chen. Strong Solutions of Navier-Stokes-Poisson Equations for Compressible Non-Newtonian Fluids. Sci J Appl Math Stat. 2016;4(4):134-140. doi: 10.11648/j.sjams.20160404.13
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.sjams.20160404.13,
author = {Yukun Song and Yang Chen},
title = {Strong Solutions of Navier-Stokes-Poisson Equations for Compressible Non-Newtonian Fluids},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {4},
number = {4},
pages = {134-140},
doi = {10.11648/j.sjams.20160404.13},
url = {https://doi.org/10.11648/j.sjams.20160404.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160404.13},
abstract = {This paper study the Navier-Stoke-Poisson equations for compressible non-Newtonian fluids in one dimensional bounded intervals. The motion of the fluid is driven by the compressible viscous isentropic flow under the self-gravitational and an external force. The local existence and uniqueness of strong solutions was proved based on some compatibility condition. The main condition is that the initial density vacuum is allowed.},
year = {2016}
}
TY - JOUR T1 - Strong Solutions of Navier-Stokes-Poisson Equations for Compressible Non-Newtonian Fluids AU - Yukun Song AU - Yang Chen Y1 - 2016/06/30 PY - 2016 N1 - https://doi.org/10.11648/j.sjams.20160404.13 DO - 10.11648/j.sjams.20160404.13 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 134 EP - 140 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20160404.13 AB - This paper study the Navier-Stoke-Poisson equations for compressible non-Newtonian fluids in one dimensional bounded intervals. The motion of the fluid is driven by the compressible viscous isentropic flow under the self-gravitational and an external force. The local existence and uniqueness of strong solutions was proved based on some compatibility condition. The main condition is that the initial density vacuum is allowed. VL - 4 IS - 4 ER -
Information
Email: