Tokyo Journal of Mathematics
- Tokyo J. Math.
- Volume 35, Number 1 (2012), 97-138.
Small-time Existence of a Strong Solution of Primitive Equations for the Ocean
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  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.
Tokyo J. Math., Volume 35, Number 1 (2012), 97-138.
First available in Project Euclid: 19 July 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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