American Institute of Mathematical Sciences

Advanced
January  2004, 11(1): 113-130. doi: 10.3934/dcds.2004.11.113

Global in time weak solutions for compressible barotropic self-gravitating fluids

Bernard Ducomet 1, , Eduard Feireisl 2, , Hana Petzeltová 2, and  Ivan Straškraba 2,

1. 

Département de physique théorique et appliquée, CEA, B.P. 12, Bruyères-le-Châtel, France
2. 

Mathematical Institute AV ČR, Žitná 25, 115 67 Praha 1, Czech Republic, Czech Republic

Received  December 2002 Revised  September 2003 Published  April 2004

The existence of global in time weak solutions to the Navier-Stokes-Poisson system of barotropic compressible flow is proved. The system takes into account the effect of self-gravitation. Moreover, the case of a non-monotone pressure important in certain applications in astrophysics and the theory of nuclear fluids is included.
Keywords: global in time solutions., Compressible self-gravitating fluid, Navier-Stokes-Poisson system.
Mathematics Subject Classification: 35Q30, 35B9.
Citation: Bernard Ducomet, Eduard Feireisl, Hana Petzeltová, Ivan Straškraba. Global in time weak solutions for compressible barotropic self-gravitating fluids. Discrete & Continuous Dynamical Systems - A, 2004, 11 (1) : 113-130. doi: 10.3934/dcds.2004.11.113
[1]

Zhong Tan, Yong Wang, Xu Zhang. Large time behavior of solutions to the non-isentropic compressible Navier-Stokes-Poisson system in $\mathbb{R}^{3}$. Kinetic & Related Models, 2012, 5 (3) : 615-638. doi: 10.3934/krm.2012.5.615
[2]

Yinxia Wang, Hengjun Zhao. Global existence and decay estimate of classical solutions to the compressible viscoelastic flows with self-gravitating. Communications on Pure & Applied Analysis, 2018, 17 (2) : 347-374. doi: 10.3934/cpaa.2018020
[3]

René Pinnau, Oliver Tse. On a regularized system of self-gravitating particles. Kinetic & Related Models, 2014, 7 (3) : 591-604. doi: 10.3934/krm.2014.7.591
[4]

Min Li, Xueke Pu, Shu Wang. Quasineutral limit for the quantum Navier-Stokes-Poisson equations. Communications on Pure & Applied Analysis, 2017, 16 (1) : 273-294. doi: 10.3934/cpaa.2017013
[5]

Yulan Xu, Yanping Dou. Large BV solutions to Euler equations in the isothermal self-gravitating gases with damping. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1451-1467. doi: 10.3934/cpaa.2009.8.1451
[6]

Haibo Cui, Zhensheng Gao, Haiyan Yin, Peixing Zhang. Stationary waves to the two-fluid non-isentropic Navier-Stokes-Poisson system in a half line: Existence, stability and convergence rate. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4839-4870. doi: 10.3934/dcds.2016009
[7]

Yingshan Chen, Shijin Ding, Wenjun Wang. Global existence and time-decay estimates of solutions to the compressible Navier-Stokes-Smoluchowski equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5287-5307. doi: 10.3934/dcds.2016032
[8]

Peixin Zhang, Jianwen Zhang, Junning Zhao. On the global existence of classical solutions for compressible Navier-Stokes equations with vacuum. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 1085-1103. doi: 10.3934/dcds.2016.36.1085
[9]

Renjun Duan, Xiongfeng Yang. Stability of rarefaction wave and boundary layer for outflow problem on the two-fluid Navier-Stokes-Poisson equations. Communications on Pure & Applied Analysis, 2013, 12 (2) : 985-1014. doi: 10.3934/cpaa.2013.12.985
[10]

Yulan Wang. Global solvability in a two-dimensional self-consistent chemotaxis-Navier-Stokes system. Discrete & Continuous Dynamical Systems - S, 2020, 13 (2) : 329-349. doi: 10.3934/dcdss.2020019
[11]

Hong Cai, Zhong Tan, Qiuju Xu. Time periodic solutions to Navier-Stokes-Korteweg system with friction. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 611-629. doi: 10.3934/dcds.2016.36.611
[12]

Weike Wang, Xin Xu. Large time behavior of solution for the full compressible navier-stokes-maxwell system. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2283-2313. doi: 10.3934/cpaa.2015.14.2283
[13]

Zoran Grujić. Regularity of forward-in-time self-similar solutions to the 3D Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 837-843. doi: 10.3934/dcds.2006.14.837
[14]

Xulong Qin, Zheng-An Yao. Global solutions of the free boundary problem for the compressible Navier-Stokes equations with density-dependent viscosity. Communications on Pure & Applied Analysis, 2010, 9 (4) : 1041-1052. doi: 10.3934/cpaa.2010.9.1041
[15]

Huicheng Yin, Lin Zhang. The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball, Ⅱ: 3D Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1063-1102. doi: 10.3934/dcds.2018045
[16]

Fei Jiang, Song Jiang, Junpin Yin. Global weak solutions to the two-dimensional Navier-Stokes equations of compressible heat-conducting flows with symmetric data and forces. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 567-587. doi: 10.3934/dcds.2014.34.567
[17]

Bingyuan Huang, Shijin Ding, Huanyao Wen. Local classical solutions of compressible Navier-Stokes-Smoluchowski equations with vacuum. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1717-1752. doi: 10.3934/dcdss.2016072
[18]

Zhilei Liang. Convergence rate of solutions to the contact discontinuity for the compressible Navier-Stokes equations. Communications on Pure & Applied Analysis, 2013, 12 (5) : 1907-1926. doi: 10.3934/cpaa.2013.12.1907
[19]

Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602
[20]

Hammadi Abidi, Taoufik Hmidi, Sahbi Keraani. On the global regularity of axisymmetric Navier-Stokes-Boussinesq system. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 737-756. doi: 10.3934/dcds.2011.29.737

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (28)
  • HTML views (0)
  • Cited by (39)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences