Geodesic
On solvability of one alpha-model of fluid motion with memory
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 78-84.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study a weak solvability of one alpha-model for non-Newtonian hydrodynamics. If the parameter alpha equals zero, then the considered alpha-model coincides with the classical model describing the motion of a fluid with memory. This model takes into account the fluid's memory along the trajectory. Additionally, we show that solutions of the alpha-model tend to solutions to the classical model as the parameter alpha tends to zero.
Keywords: non-Newtonian hydrodynamics, alpha-model, fluid with memory, existence theorem, regular lagrangian flow. 
@article{IVM_2018_6_a6,
     author = {A. V. Zvyagin and V. G. Zvyagin and D. M. Polyakov},
     title = {On solvability of one alpha-model of fluid motion with memory},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {78--84},
     publisher = {mathdoc},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_6_a6/}
}
TY  - JOUR
AU  - A. V. Zvyagin
AU  - V. G. Zvyagin
AU  - D. M. Polyakov
TI  - On solvability of one alpha-model of fluid motion with memory
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 78
EP  - 84
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_6_a6/
LA  - ru
ID  - IVM_2018_6_a6
ER  - 
%0 Journal Article
%A A. V. Zvyagin
%A V. G. Zvyagin
%A D. M. Polyakov
%T On solvability of one alpha-model of fluid motion with memory
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 78-84
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2018_6_a6/
%G ru
%F IVM_2018_6_a6
A. V. Zvyagin; V. G. Zvyagin; D. M. Polyakov. On solvability of one alpha-model of fluid motion with memory. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 78-84. http://geodesic.mathdoc.fr/item/IVM_2018_6_a6/

[1] Vorotnikov D. A., “Global generalized solutions for Maxwell-alpha and Euler-alpha equations”, Nonlinearity, 25:2 (2012), 309–327 | DOI | MR

[2] Zvyagin A. V., Polyakov D. M., “O razreshimosti alfa-modeli Dzheffrisa–Oldroida”, Differents. uravneniya, 52:6 (2016), 782–787 | DOI | MR

[3] Zvyagin V. G., Dmitrienko V. T., “O slabykh resheniyakh nachalno-kraevoi zadachi dlya uravneniya dvizheniya vyazkouprugoi zhidkosti”, Dokl. RAN, 380:3 (2001), 308–311 | MR

[4] Zvyagin V. G., Dmitrienko V. T., “O slabykh resheniyakh regulyarizovannoi modeli vyazkouprugoi zhidkosti”, Differents. uravneniya, 38:12 (2002), 1633–1645 | MR

[5] Crippa G., de Lellis C., “Estimates and regularity results for the diPerna–Lions flow”, J. Reine Angew. Math., 616 (2008), 15–46 | MR

[6] DiPerna R. J., Lions P. L., “Ordinary differential equations, transport theory and Sobolev spaces”, Invent. Math., 98 (1989), 511–547 | DOI | MR

[7] Zvyagin V. G., Orlov V. P., “O slaboi razreshimosti zadachi vyazkouprugosti s pamyatyu”, Differents. uravneniya, 53:2 (2017), 215–220 | DOI

[8] Fursikov A. V., Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999

[9] Zvyagin V. G., Turbin M. V., Matematicheskie voprosy gidrodinamiki vyazkouprugikh sred, KRASAND URSS, M., 2012

[10] Temam R., Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1971

[11] Zvyagin V. G., “Topological approximation approach to study of mathematical problems of hydrodynamics”, J. Math. Sci., 201:6 (2014), 830–858 | DOI | MR