Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
Volume 14, Issue 11, Pages 4069-4092Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdss.2020414
Keywords
Viscoelastic fluids; slightly compressible liquids; pressure waves; dispersion; Bernoulli principle; existence of weak solutions; uniqueness
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Funding
- Czech Science Foundation [19-04956S]
- FWF/CSF project I [4052 N32]
- BMBWF through the OeAD-WTZ project [CZ04/2019]
- [RVO: 61388998]
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A new concept of semi-compressible fluids is introduced for slightly compressible visco-elastic fluids, with physically consistent fully Eulerian models devised to describe the characteristics of these fluids.
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.
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