Geodesic
Existence of Global Solutions to Multidimensional Equations for Bingham Fluids
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 560-577.

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

We consider equations describing the multidimensional motion of compressible viscous (non-Newtonian) Bingham-type fluids, i.e., fluids with multivalued function relating the stresses to the tensor of strain rates. We prove the global existence theorem in time and in the initial data for the first initial boundary-value problem corresponding to flows in a bounded domain in the class of “weak” generalized solutions. In this case, we admit an anisotropic relation between the stress and strain rate tensors and study admissible relations of this kind in detail.
Keywords: compressible viscous (non-Newtonian) Bingham-type fluid, global existence theorem, initial boundary-value problem, weak generalized solution, Orlicz space. 
@article{MZM_2007_82_4_a10,
     author = {A. E. Mamontov},
     title = {Existence of {Global} {Solutions} to {Multidimensional} {Equations} for {Bingham} {Fluids}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {560--577},
     publisher = {mathdoc},
     volume = {82},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a10/}
}
TY  - JOUR
AU  - A. E. Mamontov
TI  - Existence of Global Solutions to Multidimensional Equations for Bingham Fluids
JO  - Matematičeskie zametki
PY  - 2007
SP  - 560
EP  - 577
VL  - 82
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a10/
LA  - ru
ID  - MZM_2007_82_4_a10
ER  - 
%0 Journal Article
%A A. E. Mamontov
%T Existence of Global Solutions to Multidimensional Equations for Bingham Fluids
%J Matematičeskie zametki
%D 2007
%P 560-577
%V 82
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a10/
%G ru
%F MZM_2007_82_4_a10
A. E. Mamontov. Existence of Global Solutions to Multidimensional Equations for Bingham Fluids. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 560-577. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a10/

[1] E. C. Bingham, Fluidity and Plasticity, McGrew–Hill Book Co., New York, 1922

[2] W. Prager, Introduction to Mechanics of Continua, Introductions to Higher Mathematics, Ginn and Co., New York, 1961 | MR | Zbl

[3] Dzh. Serrin, Matematicheskie osnovy klassicheskoi mekhaniki zhidkosti, IL, M., 1963 | MR

[4] D. Prasad, H. K. Kytomaa, “Particle stress and viscous compaction during shear of dense suspensions”, Intern. J. of Multiphase Flow, 21:5 (1995), 775–785 | DOI | Zbl

[5] L. E. Malvern, Introduction to the Mechanics of a Continuous Medium, Prentice–Hall, Inc. Englewood Cliffs, New Jersey, 1969

[6] I. V. Basov, V. V. Shelukhin, “Generalized solutions to the equations of compressible Bingham flows”, ZAMM Z. Angew. Math. Mech., 79:3 (1999), 185–192 | 3.0.CO;2-N class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[7] V. V. Shelukhin, “Bingham viscoplastic as a limit of non-newtonian fluids”, J. Math. Fluid Mech., 4:2 (2002), 109–127 | DOI | MR | Zbl

[8] J. Málek, M. Růžička, V. V. Shelukhin, “Hershel–Bulkley fluids: existence and regularity of steady flows”, Math. Models Methods Appl. Sci., 15:12 (2005), 1845–1861 | DOI | MR | Zbl

[9] A. E. Mamontov, “O globalnoi razreshimosti mnogomernykh uravnenii Nave–Stoksa szhimaemoi nelineino vyazkoi zhidkosti. I”, Sib. matem. zhurn., 40:2 (1999), 408–420 | MR | Zbl

[10] A. E. Mamontov, “O globalnoi razreshimosti mnogomernykh uravnenii Nave–Stoksa szhimaemoi nelineino vyazkoi zhidkosti. II”, Sib. matem. zhurn., 40:3 (1999), 635–649 | MR | Zbl

[11] M. A. Krasnoselskii, Ya. B. Rutitskii, Vypuklye funktsii i prostranstva Orlicha, Sovremennye problemy matematiki, Fizmatgiz, M., 1958 | MR | Zbl

[12] A. E. Mamontov, “Otsenki globalnoi regulyarnosti dlya mnogomernykh uravnenii szhimaemoi nenyutonovskoi zhidkosti”, Matem. zametki, 68:3 (2000), 360–376 | MR | Zbl

[13] A. V. Kazhikhov, A. E. Mamontov, “Ob odnom klasse vypuklykh funktsii i tochnykh klassakh korrektnosti zadachi Koshi dlya uravneniya perenosa v prostranstvakh Orlicha”, Sib. matem. zhurn., 39:4 (1998), 831–850 | MR | Zbl

[14] Zh.-L. Lions, Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR | Zbl

[15] R. Rokafellar, Vypuklyi analiz, Mir, M., 1973 | MR | Zbl