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| Time Discrete Approximation of Weak Solutions to Stochastic Equations of Geophysical Fluid Dynamics and Applications |
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Citation： |
Nathan GLATT-HOLTZ,Roger TEMAM,Chuntian WANG.Time Discrete Approximation of Weak Solutions to Stochastic Equations of Geophysical Fluid Dynamics and Applications[J].Chinese Annals of Mathematics B,2017,38(2):425~472 |
| Page view： 711
Net amount： 774 |
Authors： |
Nathan GLATT-HOLTZ; Roger TEMAM;Chuntian WANG |
Foundation： |
This work was supported by
the National Science Foundation under the grants NSF-DMS-1206438
and NSF-DHS-1510249, the Research Fund of Indiana University and the
National Science Foundation under the grants NSF-DMS-1004638 and
NSF-DMS-1313272. |
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| Abstract： |
As a first step towards the numerical analysis of the stochastic
primitive equations of the atmosphere and the oceans, the time
discretization of these equations by an implicit Euler scheme is
studied. From the deterministic point of view, the 3D primitive
equations are studied in their full form on a general domain and
with physically realistic boundary conditions. From the
probabilistic viewpoint, this paper deals with a wide class of
nonlinear, state dependent, white noise forcings which may be
interpreted in either the It\^{o} or the Stratonovich sense. The
proof of convergence of the Euler scheme, which is carried out
within an abstract framework, covers the equations for the oceans,
the atmosphere, the coupled oceanic-atmospheric system as well as
other related geophysical equations. The authors obtain the
existence of solutions which are weak in both the PDE and
probabilistic sense, a result which is new by itself to the best of
our knowledge. |
Keywords： |
Nonlinear stochastic partial differential equations, Geophysicalfluid dynamics, Primitive equations, Discrete time approximation,Martingale solutions, Numerical analysis of stochastic PDEs |
Classification： |
35Q86, 60H15, 35Q35 |
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