scholarly journals On the backward uniqueness of the stochastic primitive equations with additive noise

2019 ◽  
Vol 24 (7) ◽  
pp. 3157-3174
Author(s):  
Boling Guo ◽  
◽  
Guoli Zhou ◽  
Keyword(s):  
Additive Noise ◽  
Primitive Equations ◽  
Backward Uniqueness

STOCHASTIC SOLUTIONS OF THE TWO-DIMENSIONAL PRIMITIVE EQUATIONS OF THE OCEAN AND ATMOSPHERE WITH AN ADDITIVE NOISE

2007 ◽  
Vol 05 (02) ◽  
pp. 183-198 ◽  
Author(s):  
B. EWALD ◽  
M. PETCU ◽  
R. TEMAM
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
White Noise ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Point Of View ◽  
Primitive Equations ◽  
Two Dimensional ◽  
Partial Differential

The aim of this article is to establish the existence and uniqueness of stochastic solutions of the two-dimensional equations of the ocean and atmosphere. White noise is additive, and the solutions are strong in the probabilistic sense. Finally, from the point of view of partial differential equations, they are of the type z-weak, that is, bounded in L∞(L2) together with their derivative in z.

RANDOM ATTRACTOR FOR THE 3D VISCOUS STOCHASTIC PRIMITIVE EQUATIONS WITH ADDITIVE NOISE

2009 ◽  
Vol 09 (02) ◽  
pp. 293-313 ◽  
Author(s):  
HONGJUN GAO ◽  
CHENGFENG SUN
Keyword(s):  
White Noise ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Strong Solutions ◽  
Random Attractor ◽  
Primitive Equations ◽  
Additive White Noise

In this article, we obtain the existence and uniqueness of strong solutions to 3D viscous stochastic primitive equations (PEs) and the random attractor for 3D viscous PEs with additive white noise.

A METHOD FOR AUTOMATIC BLIND ESTIMATION OF ADDITIVE NOISE VARIANCE IN DIGITAL IMAGES

2010 ◽  
Vol 69 (19) ◽  
pp. 1681-1702
Author(s):  
V. V. Lukin ◽  
S. K. Abramov ◽  
A. V. Popov ◽  
P. Ye. Eltsov ◽  
Benoit Vozel ◽  
...  
Keyword(s):  
Additive Noise ◽  
Digital Images ◽  
Blind Estimation ◽  
Noise Variance

Simplified analysis of a stochastic system

1979 ◽  
Vol 44 (2) ◽  
pp. 328-339
Author(s):  
Vladimír Herles
Keyword(s):  
Statistical Analysis ◽  
Dynamic Behavior ◽  
Stochastic System ◽  
Additive Noise ◽  
Random Parameter ◽  
Systematic Difference ◽  
Order System ◽  
Constant Parameter ◽  
Random Parameters ◽  
Simplified Analysis

Contradictious results published by different authors about the dynamics of systems with random parameters have been examined. Statistical analysis of the simple 1st order system proves that the random parameter can cause a systematic difference in the dynamic behavior that cannot be (in general) described by the usual constant-parameter model with the additive noise at the output.

scholarly journals Global Well-Posedness of the Ocean Primitive Equations with Nonlinear Thermodynamics

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Peter Korn
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Boussinesq Equations ◽  
Climate Science ◽  
Rational Functions ◽  
Ocean Dynamics ◽  
Global Ocean ◽  
Primitive Equations ◽  
Well Posedness ◽  
Nonlinear Thermodynamics

AbstractWe consider the hydrostatic Boussinesq equations of global ocean dynamics, also known as the “primitive equations”, coupled to advection–diffusion equations for temperature and salt. The system of equations is closed by an equation of state that expresses density as a function of temperature, salinity and pressure. The equation of state TEOS-10, the official description of seawater and ice properties in marine science of the Intergovernmental Oceanographic Commission, is the most accurate equations of state with respect to ocean observation and rests on the firm theoretical foundation of the Gibbs formalism of thermodynamics. We study several specifications of the TEOS-10 equation of state that comply with the assumption underlying the primitive equations. These equations of state take the form of high-order polynomials or rational functions of temperature, salinity and pressure. The ocean primitive equations with a nonlinear equation of state describe richer dynamical phenomena than the system with a linear equation of state. We prove well-posedness for the ocean primitive equations with nonlinear thermodynamics in the Sobolev space $${{\mathcal {H}}^{1}}$$ H 1 . The proof rests upon the fundamental work of Cao and Titi (Ann. Math. 166:245–267, 2007) and also on the results of Kukavica and Ziane (Nonlinearity 20:2739–2753, 2007). Alternative and older nonlinear equations of state are also considered. Our results narrow the gap between the mathematical analysis of the ocean primitive equations and the equations underlying numerical ocean models used in ocean and climate science.

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