Roubíček, Tomáš From quasi-incompressible to semi-compressible fluids. (English) Zbl 1502.35125 Discrete Contin. Dyn. Syst., Ser. S 14, No. 11, 4069-4092 (2021). Summary: 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. Cited in 5 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76A10 Viscoelastic fluids 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 76N30 Waves in compressible fluids 76R50 Diffusion 35K55 Nonlinear parabolic equations 35D30 Weak solutions to PDEs 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness Keywords:viscoelastic fluids; slightly compressible liquids; pressure waves; dispersion; Bernoulli principle; existence of weak solutions; uniqueness PDFBibTeX XMLCite \textit{T. Roubíček}, Discrete Contin. Dyn. Syst., Ser. 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