Geodesic
On the solutions of Cauchy problem for quasi-hydrodynamic system
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2020), pp. 84-96

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The coincidence of bounded in space at arbitrary instant of time homogeneously screw infinitely differentiable solutions of the Cauchy problem for quasi-hydrodynamic system and Navier-Stokes system is proved. It is shown that any smooth solution of Cauchy problem for Navier-Stokes system that obeys the generalized Gromeki-Beltrami condition, as well as some boundedness conditions in space, satisfies to quasi-hydrodynamic system. Examples of solutions are given. The formulation of an unsolved problem is given, in which it is required to prove the existence and uniqueness of a smooth solution of Cauchy problem for the quasi-hydrodynamic system.
Keywords: Navier-Stokes system, Cauchy problem, homogeneously screw solutions, generalized Gormeki-Beltrami condition.
Mots-clés : quasi-hydrodynamic system 
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     author = {Yu. V. Sheretov},
     title = {On the solutions of {Cauchy} problem for quasi-hydrodynamic system},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {84--96},
     publisher = {mathdoc},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2020_1_a5/}
}
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Yu. V. Sheretov. On the solutions of Cauchy problem for quasi-hydrodynamic system. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2020), pp. 84-96. http://geodesic.mathdoc.fr/item/VTPMK_2020_1_a5/