# American Institute of Mathematical Sciences

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## From quasi-incompressible to semi-compressible fluids

 1 Mathematical Institute, Charles University, Sokolovská 83, CZ-186 75 Praha 8, Czech Republic 2 Institute of Thermomechanics, Czech Acad. Sci., Dolejškova 5, CZ-18200 Praha 8, Czech Republic

Received  December 2019 Revised  April 2020 Published  July 2020

Fund Project: This research has been partially supported from the grants 19-04956S of Czech Science Foundation, and the FWF/CSF project I 4052 N32 with BMBWF through the OeAD-WTZ project CZ04/2019, and also from the institutional support RVO: 61388998 (ČR)

A new concept of semi-compressible fluids is introduced for slightly compressible visco-elastic fluids (typically rather liquids than gasses) where mass density variations are negligible in some sense, while being directly controlled by pressure which is very small in comparison with the elastic bulk modulus. The physically consistent fully Eulerian models with specific dispersion of pressure-wave speed are devised. This contrasts to the so-called quasi-incompressible fluids which are described not physically consistently and, in fact, only approximate ideally incompressible ones in the limit. After surveying and modifying models for the quasi-incompressible fluids, we eventually devise some fully convective models complying with energy conservation and capturing phenomena as pressure-wave propagation with wave-length (and possibly also pressure) dependent velocity.

Citation: Tomáš Roubíček. From quasi-incompressible to semi-compressible fluids. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020414
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