Communications in Mathematical Physics

, Volume 214, Issue 2, pp 287–313 | Cite as

Natural Convection with Dissipative Heating

  • Y. Kagei
  • M. Růžička
  • G. Thäter


We derive a system of equations which models the motion of linear viscous fluids that undergo isochoric motions in isothermal processes but not necessarily isochoric ones in non-isothermal processes. The main point is that in contrast to the usual Oberbeck–Boussinesq approximation we do not neglect dissipative heating. We study Rayleigh–Bénard convection for our system and investigate existence, uniqueness and regularity of solutions and conditions for the stability of the motionless state.


Convection Natural Convection Viscous Fluid Boussinesq Approximation Isothermal Process 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Y. Kagei
    • 1
  • M. Růžička
    • 2
  • G. Thäter
    • 3
  1. 1.Graduate School of Mathematics, Kyushu University 36, Fukuoka 812-8581, JapanJP
  2. 2.Institute of Applied Mathematics, University of Freiburg, Eckerstr. 1, 79104 Freiburg, GermanyDE
  3. 3.Mathematical Seminar, University of Bonn, Nußallee 15, 53115 Bonn, Germany. E-mail: gudrun@msl.uni-bonn.deDE

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