Symmetries in equations of incompressible viscoelastic Maxwell medium*

Standard

Symmetries in equations of incompressible viscoelastic Maxwell medium^*. / Pukhnachev, Vladislav V.; Fominykh, Elena Yu.

In: Lithuanian Mathematical Journal, Vol. 58, No. 3, 01.07.2018, p. 309-319.

Research output: Contribution to journal › Article › peer-review

Harvard

Pukhnachev, VV & Fominykh, EY 2018, 'Symmetries in equations of incompressible viscoelastic Maxwell medium^*', Lithuanian Mathematical Journal, vol. 58, no. 3, pp. 309-319. https://doi.org/10.1007/s10986-018-9401-8

APA

Pukhnachev, V. V., & Fominykh, E. Y. (2018). Symmetries in equations of incompressible viscoelastic Maxwell medium^*. Lithuanian Mathematical Journal, 58(3), 309-319. https://doi.org/10.1007/s10986-018-9401-8

Vancouver

Pukhnachev VV, Fominykh EY. Symmetries in equations of incompressible viscoelastic Maxwell medium^*. Lithuanian Mathematical Journal. 2018 Jul 1;58(3):309-319. doi: 10.1007/s10986-018-9401-8

Author

Pukhnachev, Vladislav V. ; Fominykh, Elena Yu. / Symmetries in equations of incompressible viscoelastic Maxwell medium^*. In: Lithuanian Mathematical Journal. 2018 ; Vol. 58, No. 3. pp. 309-319.

BibTeX

@article{d23c86e3992b4a22bbea1df8ed63d186,

title = "Symmetries in equations of incompressible viscoelastic Maxwell medium*",

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.",

keywords = "invariant solutions, Johnson–Segalman objective derivative, Lie group, Maxwell medium, viscoelastic fluid",

author = "Pukhnachev, {Vladislav V.} and Fominykh, {Elena Yu}",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2018",

month = jul,

day = "1",

doi = "10.1007/s10986-018-9401-8",

language = "English",

volume = "58",

pages = "309--319",

journal = "Lithuanian Mathematical Journal",

issn = "0363-1672",

publisher = "Springer GmbH & Co, Auslieferungs-Gesellschaf",

number = "3",

}

RIS

TY - JOUR

T1 - Symmetries in equations of incompressible viscoelastic Maxwell medium*

AU - Pukhnachev, Vladislav V.

AU - Fominykh, Elena Yu

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

KW - invariant solutions

KW - Johnson–Segalman objective derivative

KW - Lie group

KW - Maxwell medium

KW - viscoelastic fluid

UR - http://www.scopus.com/inward/record.url?scp=85053458916&partnerID=8YFLogxK

U2 - 10.1007/s10986-018-9401-8

DO - 10.1007/s10986-018-9401-8

M3 - Article

AN - SCOPUS:85053458916

VL - 58

SP - 309

EP - 319

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

SN - 0363-1672

IS - 3

ER -

ID: 16601442