Well-Posedness and Stability for the Viscous Primitive Equations of Geophysics in Critical Fourier-Besov-Morrey Spaces

2020 ◽  
pp. 123-140
Author(s):  
A. Abbassi ◽  
C. Allalou ◽  
Y. Oulha
Keyword(s):  
Morrey Spaces ◽  
Primitive Equations ◽  
Well Posedness

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.

scholarly journals The hydrostatic Stokes semigroup and well-posedness of the primitive equations on spaces of bounded functions

2020 ◽  
Vol 279 (3) ◽  
pp. 108561 ◽  
Author(s):  
Yoshikazu Giga ◽  
Mathis Gries ◽  
Matthias Hieber ◽  
Amru Hussein ◽  
Takahito Kashiwabara
Keyword(s):  
Primitive Equations ◽  
Well Posedness ◽  
Bounded Functions

Well-posedness for the stochastic 2D primitive equations with Lévy noise

2013 ◽  
Vol 56 (8) ◽  
pp. 1629-1645 ◽  
Author(s):  
ChengFeng Sun ◽  
HongJun Gao
Keyword(s):  
Primitive Equations ◽  
Lévy Noise ◽  
Well Posedness ◽  
Levy Noise

scholarly journals Global strong L well-posedness of the 3D primitive equations with heat and salinity diffusion

2016 ◽  
Vol 261 (12) ◽  
pp. 6950-6981 ◽  
Author(s):  
Matthias Hieber ◽  
Amru Hussein ◽  
Takahito Kashiwabara
Keyword(s):  
Primitive Equations ◽  
Well Posedness

scholarly journals On the well-posedness of the inviscid Boussinesq equations in the Besov-Morrey spaces

2015 ◽  
Vol 8 (3) ◽  
pp. 395-411 ◽  
Author(s):  
Qunyi Bie ◽  
◽  
Qiru Wang ◽  
Zheng-An Yao ◽  
Keyword(s):  
Boussinesq Equations ◽  
Morrey Spaces ◽  
Well Posedness
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