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Science China Mathematics 2022年第6期65卷 1109-1146页

作者： Marius Paicu Ping Zhang Institut de Mathematiques de Bordeaux Universite BordeauxTalence 33405France Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

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 *** first prove the global existence of solutions to these equations under a uniform smallness assumption on the data in the Gevrey class *** we justify the limit globally-in-time from the anisotropic hyperbolic Navier-Stokes system to the hyperbolic Prandtl system with such Gevrey class 2 *** 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.

关键词： incompressible hyperbolic Navier-Stokes equations hydrostatic approximation hyperbolic Prandtl system

ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION

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Acta Mathematica Scientia 2023年第3期43卷 1081-1104页

作者：蒲学科周文利 School of Mathematics and Information Science Guangzhou UniversityGuangzhou510006China

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.

关键词： Boussinesq equations primitive equations density stratification hydrostatic approximation strong convergence

Quasi-hydrostatic Primitive Equations for Ocean Global Circulation Models

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Chinese Annals of Mathematics,Series B 2010年第6期31卷 939-952页

作者： Carine LUCAS Madalina PETCU Antoine ROUSSEAU Laboratoire MAPMO (UMR 6628) Fédération Denis Poisson (FDP-FR2964) Université d'OrléansBtiment de Mathématiques-Route de Chartres B. P. 6759 45067 Orléans Cedex 2 France Laboratoire de Mathématiques et Applications Téléport 2-B. P. 30179 Boulevard Marie et Pierre Curie 86962 Futuroscope Chasseneuil Cedex France INRIA Laboratoire Jean Kuntzmann 51 rue des Mathématiques B. P. 53 38041 Grenoble Cedex 9France

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.

关键词： hydrostatic approximation Coriolis force Ocean global circulation models Primitive equations Traditional approximation

hydrostatic LIMIT OF THE NAVIER-STOKES-ALPHA MODEL

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Acta Mathematica Scientia 2023年第5期43卷 1945-1980页

作者： Léo GLANGETAS Van-Sang NGO El Mehdi SAID Laboratoire de Mathematiques Raphael Salem Universite de Rouen NormandieCNRSUMR 6085F-76000 RouenFrance

In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin strip *** derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system... 详细信息

关键词： Navier-Stokes-αmodel hydrostatic approximation analyticity