Low stratification of a heat-conducting fluid in a time-dependent domain

Abstract

We study the low Mach number limit of the full Navier–Stokes–Fourier system in the case of low stratification with ill-prepared initial data for the problem stated on a moving domain with a prescribed motion of the boundary. Similarly as in the case of a fixed domain, we recover as a limit the Oberback–Boussinesq system; however, we identify one additional term in the temperature equation of the limit system which is related to the motion of the domain and which is not present in the case of a fixed domain. One of the main ingredients in the proof is the properties of the Helmholtz decomposition on moving domains and the dependence of eigenvalues and eigenspaces of the Neumann Laplace operator on time.

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Correspondence to Šárka Nečasová.

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The works of O.K., V.M. and Š.N. were supported by project GA16-03230S and by RVO 67985840. Last version of the paper was supported by project GA19-04243S. Part of work was done during stay of O.K. at Imperial College London which 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. Low stratification of a heat-conducting fluid in a time-dependent domain. J. Evol. Equ. (2021). https://doi.org/10.1007/s00028-020-00653-3

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