Flow of heat conducting fluid in a time-dependent domain


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.

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Corresponding author

Correspondence to Šárka Nečasová.

Additional information

The work of O.K. and Š.N. was supported by 7AMB16PL060 and by RVO 67985840. Stay of V. M. in Imperial College London was supported by GA17-01747S and RVO: 67985840. Stay of O.K. at Imperial College London was supported by the grant Iuventus Plus 0871/IP3/2016/74.

The work of A.W.-K. is partially supported by a Newton Fellowship of the Royal Society and by the grant Iuventus Plus 0871/IP3/2016/74 of Ministry of Sciences and Higher Education RP. Her stay at Institute of Mathematics of Academy of Sciences, Prague, was supported by 7AMB16PL060.

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Kreml, O., Mácha, V., Nečasová, Š. et al. Flow of heat conducting fluid in a time-dependent domain. Z. Angew. Math. Phys. 69, 119 (2018). https://doi.org/10.1007/s00033-018-1012-z

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

Mathematics Subject Classification

  • 35Q35
  • 76N10