We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations,which is obtained by using the Cattaneo type law instead of the Fourier law,evolving in a thin strip R×(0,ε).The fo...We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations,which is obtained by using the Cattaneo type law instead of the Fourier law,evolving in a thin strip R×(0,ε).The formal limit of these equations is a hyperbolic Prandtl type equation.We first prove the global existence of solutions to these equations under a uniform smallness assumption on the data in the Gevrey class 2.Then we justify the limit globally-in-time from the anisotropic hyperbolic Navier-Stokes system to the hyperbolic Prandtl system with such Gevrey class 2 data.Compared with Paicu et al.(2020)for the hydrostatic approximation of the 2-D classical Navier-Stokes system with analytic data,here the initial data belongs to the Gevrey class 2,which is very sophisticated even for the well-posedness of the classical Prandtl system(see Dietert and GerardVaret(2019)and Wang et al.(2021));furthermore,the estimate of the pressure term in the hyperbolic Prandtl system gives rise to additional difficulties.展开更多
In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin strip domain.We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit ...In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin strip domain.We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system for small initial conditions in an appropriate analytic function space.展开更多
In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongl...In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.展开更多
Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the z...Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio, is more realistic than the classical hydrostatic model, since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed. After justifying the derivation of the model, the authors provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.展开更多
基金supported by K.C.Wong Education Foundationsupported by the Agence Nationale de la Recherche,Project IFSMACS(Interaction Fluide-Structure:Modélisation,analyse,contr?le et simulation)(Grant No.ANR-15-CE40-0010)+1 种基金supported by National Basic Research Program of China(Grant No.2021YFA1000800)National Natural Science Foundation of China(Grants Nos.11731007,12031006 and 11688101)。
文摘We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations,which is obtained by using the Cattaneo type law instead of the Fourier law,evolving in a thin strip R×(0,ε).The formal limit of these equations is a hyperbolic Prandtl type equation.We first prove the global existence of solutions to these equations under a uniform smallness assumption on the data in the Gevrey class 2.Then we justify the limit globally-in-time from the anisotropic hyperbolic Navier-Stokes system to the hyperbolic Prandtl system with such Gevrey class 2 data.Compared with Paicu et al.(2020)for the hydrostatic approximation of the 2-D classical Navier-Stokes system with analytic data,here the initial data belongs to the Gevrey class 2,which is very sophisticated even for the well-posedness of the classical Prandtl system(see Dietert and GerardVaret(2019)and Wang et al.(2021));furthermore,the estimate of the pressure term in the hyperbolic Prandtl system gives rise to additional difficulties.
文摘In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin strip domain.We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system for small initial conditions in an appropriate analytic function space.
基金Pu was supported in part by the NNSF of China(11871172)the Science and Technology Projects in Guangzhou (202201020132)Zhou was supported by the Innovation Research for the Postgraduates of Guangzhou University (2021GDJC-D09)。
文摘In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.
基金supported by the ANR (No. ANR-06-BLAN0306-01)the National Science Foundation (No.NSF-DMS-0906440) and the Research Fund of Indiana University
文摘Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio, is more realistic than the classical hydrostatic model, since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed. After justifying the derivation of the model, the authors provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.
