Flow of heat conducting fluid in a time-dependent domain

  • Ondřej Kreml
  • Václav Mácha
  • Šárka NečasováEmail author
  • Aneta Wróblewska-Kamińska


We consider a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier–Stokes–Fourier system consisting of equation of continuity, momentum balance, entropy balance and energy equality. The velocity is supposed to fulfill the full-slip boundary condition and we assume that the fluid is thermally isolated. In the presented article we show the existence of a variational solution.


Compressible Navier–Stokes–Fourier equations Entropy inequality Time-varying domain Slip boundary conditions 

Mathematics Subject Classification

35Q35 76N10 


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Authors and Affiliations

  1. 1.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  2. 2.Institute of MathematicsPolish Academy of SciencesWarszawaPoland
  3. 3.Department of MathematicsImperial College LondonLondonUK

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