Symmetries in equations of incompressible viscoelastic Maxwell medium Full article
| Journal |
Lithuanian Mathematical Journal
ISSN: 0363-1672 |
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| Output data | Year: 2018, Volume: 58, Number: 3, Pages: 309-319 Pages count : 11 DOI: 10.1007/s10986-018-9401-8 | ||||
| Tags | invariant solutions; Johnson–Segalman objective derivative; Lie group; Maxwell medium; viscoelastic fluid | ||||
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Abstract:
We consider unsteady flows of incompressible viscoelastic Maxwell medium with upper, low, and Jaumann convective derivatives in the rheological constitutive law. We give characteristics of a system of equations that describe a three-dimensional motion of such a medium for all three types of convective derivative. In the general case, due to the incompressibility condition, the equations of motion have both real and complex characteristics. We study group properties of this system in the two-dimensional case. On this basis, we choose submodels of the Maxwell model that can be reduced to hyperbolic ones. The properties of the hyperbolic submodels obtained depend on the choice of the invariant derivative in the rheological relation. We also present concrete examples of invariant solutions.
Cite:
Pukhnachev V.V.
, Fominykh E.Y.
Symmetries in equations of incompressible viscoelastic Maxwell medium
Lithuanian Mathematical Journal. 2018. V.58. N3. P.309-319. DOI: 10.1007/s10986-018-9401-8 WOS Scopus РИНЦ OpenAlex
Symmetries in equations of incompressible viscoelastic Maxwell medium
Lithuanian Mathematical Journal. 2018. V.58. N3. P.309-319. DOI: 10.1007/s10986-018-9401-8 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000445103700006 |
| Scopus: | 2-s2.0-85053458916 |
| Elibrary: | 41874012 |
| OpenAlex: | W2891820796 |