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| Mathematical Analysis of the Jin-Neelin Model of El Ni\wt no-Southern-Oscillation |
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Citation： |
Yining CAO,Micka"el D. CHEKROUN,Aimin HUANG,Roger TEMAM.Mathematical Analysis of the Jin-Neelin Model of El Ni\wt no-Southern-Oscillation[J].Chinese Annals of Mathematics B,2019,40(1):1~38 |
| Page view： 1523
Net amount： 625 |
Authors： |
Yining CAO; Micka"el D. CHEKROUN;Aimin HUANG;Roger TEMAM |
Foundation： |
This work was supported by the Office of Naval Research
Multidisciplinary University Research Initiative
(No.N00014-16-1-2073), the National Science Foundation
(Nos.OCE-1658357, DMS-1616981, DMS-1206438, DMS-1510249) and the
Research Fund of Indiana University. |
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| Abstract： |
The Jin-Neelin model for the El Ni$\wt{\rm n}$o--Southern
Oscillation (ENSO for short) is considered for which the authors
establish existence and uniqueness of global solutions in time over
an unbounded channel domain. The result is proved for initial data
and forcing that are sufficiently small. The smallness conditions
involve in particular key physical parameters of the model such as
those that control the travel time of the equatorial waves and the
strength of feedback due to vertical-shear currents and upwelling;
central mechanisms in ENSO dynamics.
From the mathematical view point, the system appears as the coupling
of a linear shallow water system and a nonlinear heat equation.
Because of the very different nature of the two components of the
system, the authors find it convenient to prove the existence of
solution by semi-discretization in time and utilization of a
fractional step scheme. The main idea consists of handling the
coupling between the oceanic and temperature components by dividing
the time interval into small sub-intervals of length $k$ and on each
sub-interval to solve successively the oceanic component, using the
temperature $T$ calculated on the previous sub-interval, to then
solve the sea-surface temperature (SST for short) equation on the
current sub-interval. The passage to the limit as $k$ tends to zero
is ensured via a priori estimates derived under the aforementioned
smallness conditions. |
Keywords： |
El Ni$wt{rm n}$o--Southern Oscillation, Coupled nonlinearhyperbolic-parabolic systems, Fractional step method, Semigrouptheory |
Classification： |
35K55, 35L50, 35M33, 47D03, 76U05 |
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