Geodesic
On a Preserving Loitsyansky Invariant into Millionshtchikov Closure Model of Homogeneous Isotropic Turbulent Dynamics
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 23-37

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The existence of a solution to an initial-boundary value problem for Millionshtchikov closure model of the von Kármán–Howarth equation is proven. The behavior of the solution obtained is investigated in the limit of viscosity $\nu$ to zero. We establish the asymptotic stability of the Millionshtchikov selfsimilar solution as $t\to\infty$. Moreover, we prove that Loitsyansky integral plays the role of a conservation law for Millionshtchikov closure model of homogeneous isotropic turbulent dynamics.
Keywords: von Karman-Howarth equation, Millionshtchikov model, solvability of initial-boundary value problem, Trotter–Kato product formula.
Mots-clés : Loitsyansky invariant 
@article{VNGU_2009_9_4_a2,
     author = {V. N. Grebenev and M. Yu. Filimonov},
     title = {On a {Preserving} {Loitsyansky} {Invariant} into {Millionshtchikov} {Closure} {Model} of {Homogeneous} {Isotropic} {Turbulent} {Dynamics}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {23--37},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a2/}
}
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V. N. Grebenev; M. Yu. Filimonov. On a Preserving Loitsyansky Invariant into Millionshtchikov Closure Model of Homogeneous Isotropic Turbulent Dynamics. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 23-37. http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a2/