Geodesic
Global solvability of one-dimensional axially-symmetric micropolar fluid equations
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 67-77.

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

We prove the theorem of global existence of a weak solution to an one-dimensional initial-boundary value problem for the micropolar fluid equations under the condition of axial symmetry. The micropolar fluid model is a well-known generalization of the classical Navier—Stokes equations for the case when the rotation of the continuum particles is taken into account.
Keywords: micropolar fluid, global existence theorem, axial symmetry. . 
@article{SJIM_2021_24_1_a4,
     author = {V. V. Neverov},
     title = {Global solvability of one-dimensional axially-symmetric micropolar fluid equations},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {67--77},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a4/}
}
TY  - JOUR
AU  - V. V. Neverov
TI  - Global solvability of one-dimensional axially-symmetric micropolar fluid equations
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2021
SP  - 67
EP  - 77
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a4/
LA  - ru
ID  - SJIM_2021_24_1_a4
ER  - 
%0 Journal Article
%A V. V. Neverov
%T Global solvability of one-dimensional axially-symmetric micropolar fluid equations
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2021
%P 67-77
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a4/
%G ru
%F SJIM_2021_24_1_a4
V. V. Neverov. Global solvability of one-dimensional axially-symmetric micropolar fluid equations. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 67-77. http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a4/

[1] V. V. Shelukhin, V. V. Neverov, “Flow of micropolar and viscoplastic fluids in a Hele-Shaw cell”, J. Appl. Mech. Tech. Phys., 55:6 (2014), 905–916 | DOI | MR | Zbl

[2] E. Cosserat, F. Cosserat, Theorie des Corps Deformable, A. Hermann et fils, Paris, 1909

[3] A. C. Eringen, Microcontinuum Field Theories, v. I, II, Springer-Verl, N.Y., 1999 | MR | Zbl

[4] G. Lukaszewicz, Micropolar Fluids. Theory, Applications, Birkhäuser Boston, Boston, 1999 | MR | Zbl

[5] Bo-Qing Dong, Zhifei Zhang, “Global regularity of the 2D micropolar fluid flows with zero angular viscosity”, J. Differ. Equ., 249 (2010), 200–213 | DOI | MR | Zbl

[6] V. V. Shelukhin, M. Ružička, “On Cosserat-Bingham fluids”, Z. Angew. Math. Mech., 93:1 (2013), 57–72 | DOI | MR | Zbl

[7] V. V. Shelukhin, N. V. Chemetov, “Global solvability of the one-dimensional Cosserat-Bingham fluid equations”, J. Math. Fluid Mech., 17:3 (2015), 495–511 | DOI | MR | Zbl

[8] Zhuan Ye, “Global existence of strong solution to the 3D micropolar equations with a damping term”, Appl. Math. Lett., 83 (2018), 188–193 | DOI | MR | Zbl

[9] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Ural'ceva, Linear and Quasi-Linear Equations of Parabolic Type, Amer. Math. Soc., Providence, 1968 | MR | Zbl

[10] V. N. Monakhov, Boundary-Value Problems with Free Boundaries for Elliptic Systems of Equations, Translations of Mathematical Monographs, 57, Amer. Math. Soc., Providence, 1983 | DOI | MR | Zbl