# 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}
}
• Published 25 September 2012
• Mathematics
• Journal of Mathematical Physics
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.
11 Citations
Local Well-Posedness of Strong Solutions to the Three-Dimensional Compressible Primitive Equations
• Mathematics
• 2019
Author(s): Liu, Xin; Titi, Edriss S | Abstract: This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of
An Approach to the Primitive Equations for Oceanic and Atmospheric Dynamics by Evolution Equations
• Mathematics
• 2020
The primitive equations for oceanic and atmospheric dynamics are a fundamental model for many geophysical flows. In this chapter we present a summary of an approach to these equations based on the
On the Local Well-posedness of the Prandtl and Hydrostatic Euler Equations with Multiple Monotonicity Regions
• Mathematics
SIAM J. Math. Anal.
• 2014
A new class of data is found for which the Prandtl boundary layer equations and the hydrostatic Euler equations are locally in time well-posed and the local existence and uniqueness hold.
Almost Global Existence for the Prandtl Boundary Layer Equations
• Mathematics
• 2015
We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H1 space with respect to the normal variable, and is real-analytic with respect to the
2 RESEARCH STATEMENT Lipschitz bounds for the critical
• Mathematics
• 2017
My work is focused on problems in nonlinear PDE theory arising from geophysics, fluid dynamics, biology and material science. A significant portion of my work is devoted to local and global issues
Global Existence of Weak Solutions to the Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosities
• Mathematics
SIAM J. Math. Anal.
• 2019
We show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosities. In analogy with the case of the compres...
Local-in-Time Solvability and Space Analyticity for the Navier–Stokes Equations with BMO-Type Initial Data
It is proved that there exists a local-in-time solution $$u\in C([0,T),bmo({\mathbb {R}}^d)^d)$$ u ∈ C ( [ 0 , T ) , b m o ( R d ) d ) of the Navier–Stokes equations such that every u ( t ) has an
Zero Mach Number Limit of the Compressible Primitive Equations Part I: Well-prepared Initial Data
• Mathematics
• 2019
Author(s): Liu, Xin; Titi, Edriss S | Abstract: This work concerns the zero Mach number limit of the compressible primitive equations. The primitive equations with the incompressibility condition are
A P ] 3 1 O ct 2 01 8 Local-intime Solvability and Space Analyticity for the Navier-Stokes Equations with BMO-type Initial Data
It is proved that there exists a local-in-time solution u ∈ C([0, T ), bmo(R)) of the NavierStokes equations such that every u(t) has an analytic extension on a complex domain whose size only depends

## 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
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
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