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Transactions of the Moscow Mathematical Society

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On the Existence of a Global Solution of the Modified Navier-Stokes Equations

Author: G. M. Kobel’kov
Translated by: V. E. Nazaikinskii
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 77 (2016), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2016, 177-201
MSC (2010): Primary 76D05; Secondary 35Q30
Published electronically: November 28, 2016
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Abstract: We prove global existence theorems for initial-boundary value problems for the modified Navier-Stokes equations used when modeling ocean dynamic processes. First, the case of distinct vertical and horizontal viscosities for the Navier-Stokes equations is considered. Then a result due to Ladyzhenskaya for the modified Navier-Stokes equations is improved, whereby the elliptic operator is strengthened with respect to the horizontal variables alone and only for the horizontal momentum equations. Finally, the global existence and uniqueness of a solution is proved for the primitive equations describing the large-scale ocean dynamics.

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Additional Information

G. M. Kobel’kov
Affiliation: Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Moscow, Russia; Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

Keywords: Navier--Stokes equations, primitive equations, large-scale ocean dynamics, modification of Navier--Stokes equations, global existence.
Published electronically: November 28, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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