The primitive equations as the small aspect ratio limit of the Navier–Stokes equations: rigorous justification of the hydrostatic approximation
An important feature of the planetary oceanic dynamics is that the aspect ratio (the ratio of
the depth to horizontal width) is very small. As a result, the hydrostatic approximation …
the depth to horizontal width) is very small. As a result, the hydrostatic approximation …
Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics
C Cao, S Ibrahim, K Nakanishi, ES Titi - Communications in Mathematical …, 2015 - Springer
In an earlier work we have shown the global (for all initial data and all time) well-posedness
of strong solutions to the three-dimensional viscous primitive equations of large scale …
of strong solutions to the three-dimensional viscous primitive equations of large scale …
Strong solutions to the 3D primitive equations with only horizontal dissipation: near H1 initial data
In this paper, we consider the initial–boundary value problem of the three-dimensional
primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and …
primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and …
Global well-posedness of the 2D Boussinesq equations with vertical dissipation
We prove the global well-posedness of the two-dimensional Boussinesq equations with only
vertical dissipation. The initial data (u_0,\theta_0)(u 0, θ 0) are required to be only in the …
vertical dissipation. The initial data (u_0,\theta_0)(u 0, θ 0) are required to be only in the …
The primitive equations approximation of the anisotropic horizontally viscous 3D Navier-Stokes equations
In this paper, we provide rigorous justification of the hydrostatic approximation and the
derivation of primitive equations as the small aspect ratio limit of the incompressible three …
derivation of primitive equations as the small aspect ratio limit of the incompressible three …
Global well-posedness of strong solutions to a tropical climate model
J Li, ES Titi - arXiv preprint arXiv:1504.05285, 2015 - arxiv.org
In this paper, we consider the Cauchy problem to the TROPIC CLIMATE MODEL derived by
Frierson-Majda-Pauluis in [Comm. Math. Sci, Vol. 2 (2004)] which is a coupled system of the …
Frierson-Majda-Pauluis in [Comm. Math. Sci, Vol. 2 (2004)] which is a coupled system of the …
Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity
In this paper, we consider the 3D primitive equations of oceanic and atmospheric dynamics
with only horizontal eddy viscosities in the horizontal momentum equations and only vertical …
with only horizontal eddy viscosities in the horizontal momentum equations and only vertical …
Well-posedness of the hydrostatic Navier–Stokes equations
D Gerard-Varet, N Masmoudi, V Vicol - Analysis & PDE, 2020 - msp.org
We address the local well-posedness of the hydrostatic Navier–Stokes equations. These
equations, sometimes called reduced Navier–Stokes/Prandtl, appear as a formal limit of the …
equations, sometimes called reduced Navier–Stokes/Prandtl, appear as a formal limit of the …
Recent advances concerning certain class of geophysical flows
J Li, ES Titi - arXiv preprint arXiv:1604.01695, 2016 - arxiv.org
This paper is devoted to reviewing several recent developments concerning certain class of
geophysical models, including the primitive equations (PEs) of atmospheric and oceanic …
geophysical models, including the primitive equations (PEs) of atmospheric and oceanic …
Continuous data assimilation for the 3D primitive equations of the ocean
Y Pei - arXiv preprint arXiv:1805.06007, 2018 - arxiv.org
In this article, we show that the continuous data assimilation algorithm is valid for the 3D
primitive equations of the ocean. Namely, the $ L^ 2$ norm of the assimilated solution …
primitive equations of the ocean. Namely, the $ L^ 2$ norm of the assimilated solution …