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June 2012 Small-time Existence of a Strong Solution of Primitive Equations for the Ocean
Hirotada HONDA, Atusi TANI
Tokyo J. Math. 35(1): 97-138 (June 2012). DOI: 10.3836/tjm/1342701347


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.


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Hirotada HONDA. Atusi TANI. "Small-time Existence of a Strong Solution of Primitive Equations for the Ocean." Tokyo J. Math. 35 (1) 97 - 138, June 2012.


Published: June 2012
First available in Project Euclid: 19 July 2012

zbMATH: 1270.35326
MathSciNet: MR2977448
Digital Object Identifier: 10.3836/tjm/1342701347

Primary: 35M10
Secondary: 35Q35, 35R35, 76D99, 86A05

Rights: Copyright © 2012 Publication Committee for the Tokyo Journal of Mathematics


Vol.35 • No. 1 • June 2012
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