Issue |
ESAIM: M2AN
Volume 49, Number 3, May-June 2015
|
|
---|---|---|
Page(s) | 875 - 919 | |
DOI | https://doi.org/10.1051/m2an/2014061 | |
Published online | 16 April 2015 |
Small-time solvability of primitive equations for the ocean with spatially-varying vertical mixing
Department of Mathematics, Keio University,
3-14-1 Hiyoshi, 223-8522
Yokohama,
Japan
t.asc2904@gmail.com
Received:
1
March
2012
Revised:
6
September
2014
The small-time existence of a strong solution to the free surface problem of primitive equations for the ocean with variable turbulent viscosity terms is shown in this paper. In this model, the turbulent viscosity coefficients, which include the Richardson number depending on unknown variables, are explicitly formulated. In addition, following the formulation of practical models, the kinematic condition is assumed on the free ocean surface. As in preceding works, we consider the problem in the three-dimensional strip-like region, and assume the f-approximation. Under some conditions on the initial and boundary data and the topography of the bottom of the ocean, we construct a strong local-in-time solution in Sobolev–Slobodetskiĭ spaces. The boundedness of the temperature and salinity is also shown in the present paper.
Mathematics Subject Classification: 35M10 / 35Q35 / 35R35
Key words: Primitive equations / Sobolev–Slobodetskiĭ space / strong solution
© EDP Sciences, SMAI, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.