Local existence of solutions to the free boundary value problem for the primitive equations of the ocean
@article{Ignatova2012LocalEO, title={Local existence of solutions to the free boundary value problem for the primitive equations of the ocean}, author={Mihaela Ignatova and Igor Kukavica and Mohammed Ziane}, journal={Journal of Mathematical Physics}, year={2012}, volume={53}, pages={103101} }
Lions, Temam, and Wang in [“Probleme a frontiere libre pour les modeles couples de l'ocean et de l'atmosphere,” Acad. Sci., Paris, C. R. 318(12), 1165–1171 (1994)] introduced a free surface model for the primitive equations of the ocean. In this paper, we establish the local well-posedness of the model with analytic initial data.
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References
SHOWING 1-10 OF 40 REFERENCES
Boundary conditions for the 2D linearized PEs of the ocean in the absence of viscosity
- Mathematics
- 2005
The linearized Primitive Equations with vanishing viscosity
are considered. Some new boundary conditions (of transparent type)
are introduced in the context of a modal
expansion of the solution…
On the regularity of the primitive equations of the ocean
- Mathematics
- 2007
We prove the existence of global strong solutions of the primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side and the bottom boundaries including the varying…
Uniform gradient bounds for the primitive equations of the ocean
- Mathematics
- 2008
In this paper, we consider the 3D primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side and bottom boundaries. We provide an explicit upper bound for the H…
REGULARITY RESULTS FOR LINEAR ELLIPTIC PROBLEMS RELATED TO THE PRIMITIVE EQUATIONS
- Mathematics
- 2002
The authors study the regularity of solutions of the GFD-Stokes problem and of some second order linear elliptic partial differential equations related to the Primitive Equations of the ocean. The…
Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain
- Mathematics
- 2011
Analyticity of Solutions for a Generalized Euler Equation
- Mathematics
- 1997
Abstract We consider the so-called lake and great lake equations, which are shallow water equations that describe the long-time motion of an inviscid, incompressible fluid contained in a shallow…
Pathwise Solutions of the 2-D Stochastic Primitive Equations
- Mathematics
- 2010
In this work we consider a stochastic version of the Primitive Equations (PEs) of the ocean and the atmosphere and establish the existence and uniqueness of pathwise, strong solutions. The analysis…
Finite Dimensional Behaviors of the Primitive Equations Under Small Depth Assumption
- Mathematics
- 2007
In this article, we study the asymptotic degrees of freedom for solutions to the primitive equation (PEs for brevity). More precisely, we will prove that the long-time behavior of solutions to PEs is…
Simulations of the 2.5D inviscid primitive equations in a limited domain
- MathematicsJ. Comput. Phys.
- 2008