Tokyo Journal of Mathematics

Small-time Existence of a Strong Solution of Primitive Equations for the Ocean

Hirotada HONDA and Atusi TANI

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Abstract

Primitive equations derived originally by Richardson in 1920's have been considered as the model equations describing the motion of atmosphere, ocean and coupled atmosphere and ocean. In this paper, we discuss the free boundary problem of the primitive equations for the ocean in three-dimensional strip with surface tension. Using the so-called $p$-coordinates and a coordinate transformation similar to that in [2] in order to fix the time-dependent domain, we prove temporally local existence of the unique strong solution to the transformed problem in Sobolev-Slobodetskiĭ spaces.

Article information

Source
Tokyo J. Math., Volume 35, Number 1 (2012), 97-138.

Dates
First available in Project Euclid: 19 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1342701347

Digital Object Identifier
doi:10.3836/tjm/1342701347

Mathematical Reviews number (MathSciNet)
MR2977448

Zentralblatt MATH identifier
1270.35326

Subjects
Primary: 35M10: Equations of mixed type
Secondary: 35Q35: PDEs in connection with fluid mechanics 35R35: Free boundary problems 76D99: None of the above, but in this section 86A05: Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05]

Citation

HONDA, Hirotada; TANI, Atusi. Small-time Existence of a Strong Solution of Primitive Equations for the Ocean. Tokyo J. Math. 35 (2012), no. 1, 97--138. doi:10.3836/tjm/1342701347. https://projecteuclid.org/euclid.tjm/1342701347


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