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

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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/}
}
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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/