American Institute of Mathematical Sciences

Advanced
September  2005, 4(3): 635-664. doi: 10.3934/cpaa.2005.4.635

Exponential stability in $H^4$ for the Navier--Stokes equations of compressible and heat conductive fluid

Yuming Qin 1, , T. F. Ma 2, , M. M. Cavalcanti 2, and  D. Andrade 2,

1. 

Department of Mathematics - Henan University,Kaifeng 475001, China
2. 

Department of Mathematics - State University of Maringá, 87020-900 Maringá, PR, Brazil, Brazil, Brazil

Received  June 2004 Revised  April 2005 Published  June 2005

This paper is concerned with the exponential stability of solutions in $H^4$ for the Navier--Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains $\Omega_n$ in $\mathbb{R}^n (n=2,3)$.
Keywords: Compressible Navier--Stokes equation, spherically symmetric solutions., polytropic viscous ideal gas.
Mathematics Subject Classification: Primary: 35B30, 35B40; Secondary: 35Q7.
Citation: Yuming Qin, T. F. Ma, M. M. Cavalcanti, D. Andrade. Exponential stability in $H^4$ for the Navier--Stokes equations of compressible and heat conductive fluid. Communications on Pure & Applied Analysis, 2005, 4 (3) : 635-664. doi: 10.3934/cpaa.2005.4.635
[1]

Xinhua Zhao, Zilai Li. Asymptotic behavior of spherically or cylindrically symmetric solutions to the compressible Navier-Stokes equations with large initial data. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1421-1448. doi: 10.3934/cpaa.2020052
[2]

Wenjun Wang, Lei Yao. Spherically symmetric Navier-Stokes equations with degenerate viscosity coefficients and vacuum. Communications on Pure & Applied Analysis, 2010, 9 (2) : 459-481. doi: 10.3934/cpaa.2010.9.459
[3]

Tian Ma, Shouhong Wang. Asymptotic structure for solutions of the Navier--Stokes equations. Discrete & Continuous Dynamical Systems - A, 2004, 11 (1) : 189-204. doi: 10.3934/dcds.2004.11.189
[4]

Milan Pokorný, Piotr B. Mucha. 3D steady compressible Navier--Stokes equations. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 151-163. doi: 10.3934/dcdss.2008.1.151
[5]

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
[6]

Mustafa A. H. Al-Jaboori, D. Wirosoetisno. Navier--Stokes equations on the $\beta$-plane. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 687-701. doi: 10.3934/dcdsb.2011.16.687
[7]

D. Wirosoetisno. Navier--Stokes equations on a rapidly rotating sphere. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 1251-1259. doi: 10.3934/dcdsb.2015.20.1251
[8]

Pavel I. Plotnikov, Jan Sokolowski. Optimal shape control of airfoil in compressible gas flow governed by Navier-Stokes equations. Evolution Equations & Control Theory, 2013, 2 (3) : 495-516. doi: 10.3934/eect.2013.2.495
[9]

Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible Navier-Stokes equations with free boundary. Kinetic & Related Models, 2010, 3 (3) : 409-425. doi: 10.3934/krm.2010.3.409
[10]

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
[11]

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
[12]

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
[13]

Patrick Penel, Milan Pokorný. Improvement of some anisotropic regularity criteria for the Navier--Stokes equations. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1401-1407. doi: 10.3934/dcdss.2013.6.1401
[14]

C. Foias, M. S Jolly, O. P. Manley. Recurrence in the 2-$D$ Navier--Stokes equations. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 253-268. doi: 10.3934/dcds.2004.10.253
[15]

Kuijie Li, Tohru Ozawa, Baoxiang Wang. Dynamical behavior for the solutions of the Navier-Stokes equation. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1511-1560. doi: 10.3934/cpaa.2018073
[16]

Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602
[17]

Yuming Qin, Jianlin Zhang. Global existence and asymptotic behavior of spherically symmetric solutions for the multi-dimensional infrarelativistic model. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2529-2574. doi: 10.3934/cpaa.2019115
[18]

Boris Haspot, Ewelina Zatorska. From the highly compressible Navier-Stokes equations to the porous medium equation -- rate of convergence. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3107-3123. doi: 10.3934/dcds.2016.36.3107
[19]

Sun-Ho Choi. Weighted energy method and long wave short wave decomposition on the linearized compressible Navier-Stokes equation. Networks & Heterogeneous Media, 2013, 8 (2) : 465-479. doi: 10.3934/nhm.2013.8.465
[20]

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

2019 Impact Factor: 1.105

Tools

Metrics

  • PDF downloads (32)
  • HTML views (0)
  • Cited by (10)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences