Volume 4, Issue 4, August 2016, Page: 134-140
Strong Solutions of Navier-Stokes-Poisson Equations for Compressible Non-Newtonian Fluids
Yukun Song, College of Science, Liaoning University of Technology, Jinzhou, P. R. China
Yang Chen, College of Science, Liaoning University of Technology, Jinzhou, P. R. China
Received: Jun. 26, 2016;       Published: Jun. 30, 2016
DOI: 10.11648/j.sjams.20160404.13      View  2639      Downloads  89
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.
Keywords
Strong Solutions, Navier-Stokes-Poisson Equations, Non-Newtonian Fluids, Vacuum
To cite this article
Yukun Song, Yang Chen, Strong Solutions of Navier-Stokes-Poisson Equations for Compressible Non-Newtonian Fluids, Science Journal of Applied Mathematics and Statistics. Vol. 4, No. 4, 2016, pp. 134-140. doi: 10.11648/j.sjams.20160404.13
Reference
[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.
Browse journals by subject