• Previous Article
    Robust exponential attractors and convergence to equilibria for non-isothermal Cahn-Hilliard equations with dynamic boundary conditions
  • DCDS-S Home
  • This Issue
  • Next Article
    Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions
March  2009, 2(1): 95-111. doi: 10.3934/dcdss.2009.2.95

A stabilizing effect of a high-frequency driving force on the motion of a viscous, compressible, and heat conducting fluid

1. 

Institute of Mathematics AS ČR, Žitná 25, 115 67 Praha 1

2. 

Charles University in Prague, Faculty of Mathematics and Physics, Dept. of Mathematical Analysis, Sokolovská 83, 186 75 Praha 8

Received  August 2007 Revised  November 2008 Published  January 2009

We study the impact of an oscillating external force on the motion of a viscous, compressible, and heat conducting fluid. Assuming that the frequency of oscillations increases sufficiently fast as the time goes to infinity, the solutions are shown to stabilize to a spatially homogeneous static state.
Citation: Eduard Feireisl, Dalibor Pražák. A stabilizing effect of a high-frequency driving force on the motion of a viscous, compressible, and heat conducting fluid. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 95-111. doi: 10.3934/dcdss.2009.2.95
[1]

Deconinck Bernard, Olga Trichtchenko. High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1323-1358. doi: 10.3934/dcds.2017055

[2]

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 and Applied Analysis, 2005, 4 (3) : 635-664. doi: 10.3934/cpaa.2005.4.635

[3]

Eugenio Aulisa, Akif Ibragimov, Emine Yasemen Kaya-Cekin. Fluid structure interaction problem with changing thickness beam and slightly compressible fluid. Discrete and Continuous Dynamical Systems - S, 2014, 7 (6) : 1133-1148. doi: 10.3934/dcdss.2014.7.1133

[4]

Young-Sam Kwon, Antonin Novotny. Derivation of geostrophic equations as a rigorous limit of compressible rotating and heat conducting fluids with the general initial data. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 395-421. doi: 10.3934/dcds.2020015

[5]

Zefu Feng, Changjiang Zhu. Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3069-3097. doi: 10.3934/dcds.2019127

[6]

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 and Continuous Dynamical Systems, 2014, 34 (2) : 567-587. doi: 10.3934/dcds.2014.34.567

[7]

Youcef Amirat, Kamel Hamdache. Weak solutions to stationary equations of heat transfer in a magnetic fluid. Communications on Pure and Applied Analysis, 2019, 18 (2) : 709-734. doi: 10.3934/cpaa.2019035

[8]

Haibo Cui, Junpei Gao, Lei Yao. Asymptotic behavior of the one-dimensional compressible micropolar fluid model. Electronic Research Archive, 2021, 29 (2) : 2063-2075. doi: 10.3934/era.2020105

[9]

Eduard Feireisl, Hana Petzeltová. Low Mach number asymptotics for reacting compressible fluid flows. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 455-480. doi: 10.3934/dcds.2010.26.455

[10]

Zhi-Ying Sun, Lan Huang, Xin-Guang Yang. Exponential stability and regularity of compressible viscous micropolar fluid with cylinder symmetry. Electronic Research Archive, 2020, 28 (2) : 861-878. doi: 10.3934/era.2020045

[11]

Chiu-Ya Lan, Chi-Kun Lin. Asymptotic behavior of the compressible viscous potential fluid: Renormalization group approach. Discrete and Continuous Dynamical Systems, 2004, 11 (1) : 161-188. doi: 10.3934/dcds.2004.11.161

[12]

George Avalos, Pelin G. Geredeli, Justin T. Webster. Semigroup well-posedness of a linearized, compressible fluid with an elastic boundary. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1267-1295. doi: 10.3934/dcdsb.2018151

[13]

Lan Huang, Zhiying Sun, Xin-Guang Yang, Alain Miranville. Global behavior for the classical solution of compressible viscous micropolar fluid with cylinder symmetry. Communications on Pure and Applied Analysis, 2022, 21 (5) : 1595-1620. doi: 10.3934/cpaa.2022033

[14]

Takayuki Kubo, Yoshihiro Shibata, Kohei Soga. On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3741-3774. doi: 10.3934/dcds.2016.36.3741

[15]

George Avalos, Roberto Triggiani. Uniform stabilization of a coupled PDE system arising in fluid-structure interaction with boundary dissipation at the interface. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 817-833. doi: 10.3934/dcds.2008.22.817

[16]

Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.. Evolution Equations and Control Theory, 2014, 3 (1) : 83-118. doi: 10.3934/eect.2014.3.83

[17]

Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system.. Evolution Equations and Control Theory, 2014, 3 (1) : 59-82. doi: 10.3934/eect.2014.3.59

[18]

Mehdi Badra, Takéo Takahashi. Feedback boundary stabilization of 2d fluid-structure interaction systems. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2315-2373. doi: 10.3934/dcds.2017102

[19]

Hong Cai, Zhong Tan, Qiuju Xu. Time periodic solutions of the non-isentropic compressible fluid models of Korteweg type. Kinetic and Related Models, 2015, 8 (1) : 29-51. doi: 10.3934/krm.2015.8.29

[20]

Matthias Hieber, Miho Murata. The $L^p$-approach to the fluid-rigid body interaction problem for compressible fluids. Evolution Equations and Control Theory, 2015, 4 (1) : 69-87. doi: 10.3934/eect.2015.4.69

2021 Impact Factor: 1.865

Metrics

  • PDF downloads (63)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]