On the uniqueness of \(z\)-weak solutions of the three-dimensional primitive equations of the ocean

DOI10.1016/j.nonrwa.2009.02.031zbMath1189.35005OpenAlexW2000777954MaRDI QIDQ974549

Theodore Tachim-Medjo

Publication date: 3 June 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2009.02.031

zbMATH Keywords

strong in the vertical directionweak in the horizontal direction

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Weak solutions to PDEs (35D30) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (18)

Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity ⋮ Global well-posedness of z-weak solutions to the primitive equations without vertical diffusivity ⋮ Martingale Solutions of the Stochastic 2D Primitive Equations with Anisotropic Viscosity ⋮ Global attractors for the three-dimensional viscous primitive equations of large-scale atmosphere in log-pressure coordinate ⋮ The hydrostatic Stokes semigroup and well-posedness of the primitive equations on spaces of bounded functions ⋮ Existence and Uniqueness of Weak Solutions to Viscous Primitive Equations for a Certain Class of Discontinuous Initial Data ⋮ On energy conservation for the hydrostatic Euler equations: an Onsager conjecture ⋮ On the rigorous mathematical derivation for the viscous primitive equations with density stratification ⋮ Global existence and asymptotic stability of the free boundary problem of the primitive equations with heat insulation ⋮ Blow-up criterion of solutions of the horizontal viscous primitive equations with horizontal eddy diffusivity ⋮ Rigorous derivation of the full primitive equations by the scaled Boussinesq equations with rotation ⋮ The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation ⋮ Uniqueness of some weak solutions for 2D viscous primitive equations ⋮ Global attractor of the three-dimensional primitive equations of large-scale Ocean and atmosphere dynamics ⋮ Strong solutions to the 3D primitive equations with only horizontal dissipation: near \(H^{1}\) initial data ⋮ Pullback attractor for nonautonomous primitive equations of large-scale ocean and atmosphere dynamics ⋮ Averaging of a 3D primitive equations with oscillating external forces ⋮ Approximation of stationary statistical properties of the three-dimensional primitive equations of large-scale ocean and atmosphere dynamics

Cites Work

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• Regularity results for linear elliptic problems related to the primitive equations.
• On the backward uniqueness of the primitive equations
• On the three-dimensional primitive equations
• Multi-layer quasi-geostrophic equations of the ocean with delays
• Existence and regularity results for the primitive equations in two space dimensions
• On mathematical problems for the primitive equations of the ocean: The mesoscale midlatitude case
• Asymptotic analysis of the primitive equations under the small depth assumption
• Anisotropic estimates and strong solutions of the primitive equations.
• The primitive equations on the large scale ocean under the small depth hypothesis.
• Navier-Stokes equations in three-dimensional thin domains with various boundary conditions
• Mathematical theory for the coupled atmosphere-ocean models (CAO III)
• Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics
• Existence of a solution `in the large' for the 3D large-scale ocean dynamics equations
• On the order of magnitude of the baroclinic flow in the primitive equations of the ocean
• The global attractor for the solutions to the 3D viscous primitive equations
• On the equations of the large-scale ocean
• Barotropic-Baroclinic Formulation of the Primitive Equations of the Ocean
• Attractors for the multilayer quasi-geostrophic equations of the ocean with delays
• Higher Order Approximation Equations for the Primitive Equations of the Ocean
• Barotropic-Baroclinic Time Splitting for the Primitive Equations of the Ocean

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