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In these lectures, we will focus on the analysis of oceanographic models. These models involve several small parameters: Mach number, Froude number, Rossby number... We will present a hierarchy of models, and explain how they can formally be derived from one another. We will also present different mathematical tools to address the asymptotic analysis of these models (filtering methods, boundary layer techniques).

86A05 ; 34E13 ; 35Q30 ; 35Q86 ; 35Jxx

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In these lectures, we will focus on the analysis of oceanographic models. These models involve several small parameters: Mach number, Froude number, Rossby number... We will present a hierarchy of models, and explain how they can formally be derived from one another. We will also present different mathematical tools to address the asymptotic analysis of these models (filtering methods, boundary layer techniques).

86A05 ; 34E13 ; 35Q30 ; 35Q86 ; 35Jxx

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Déposez votre fichier ici pour le déplacer vers cet enregistrement.

In these lectures, we will focus on the analysis of oceanographic models. These models involve several small parameters: Mach number, Froude number, Rossby number... We will present a hierarchy of models, and explain how they can formally be derived from one another. We will also present different mathematical tools to address the asymptotic analysis of these models (filtering methods, boundary layer techniques).

86A05 ; 34E13 ; 35Q30 ; 35Q86 ; 35Jxx

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The purpose of this talk is to present two 1d congestion models: a soft congestion model with a singular pressure, and a hard congestion model in which the dynamic is different in the congested and non-congested zone (incompressible vs. compressible dynamic). The hard congested model is the limit of the soft one as the parameter within the singular presure vanishes.
For each model, we prove the existence of traveling waves, and we study their stability. This is a joint work with Charlotte Perrin.[-]

The purpose of this talk is to present two 1d congestion models: a soft congestion model with a singular pressure, and a hard congestion model in which the dynamic is different in the congested and non-congested zone (incompressible vs. compressible dynamic). The hard congested model is the limit of the soft one as the parameter within the singular presure vanishes.
For each model, we prove the existence of traveling waves, and we study their ...[+]

35B35 ; 35Q35 ; 35R35

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The purpose of these lectures is to present general methods to construct boundary layers both in linear and nonlinear contexts. We will explain how the boundary layer sizes and profiles can be predicted in linear cases, together with some decay estimates. We will illustrate this method with several explicit examples: Ekman layers, reflection of internal waves in a stratified fluid. . . We will also tackle semilinear problems, adding for instance a convection term to the previous examples. Eventually, we will introduce some tools for the study of the Prandtl equation.[-]

The purpose of these lectures is to present general methods to construct boundary layers both in linear and nonlinear contexts. We will explain how the boundary layer sizes and profiles can be predicted in linear cases, together with some decay estimates. We will illustrate this method with several explicit examples: Ekman layers, reflection of internal waves in a stratified fluid. . . We will also tackle semilinear problems, adding for instance ...[+]

35Q35 ; 35Q86 ; 76D10

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The purpose of these lectures is to present general methods to construct boundary layers both in linear and nonlinear contexts. We will explain how the boundary layer sizes and profiles can be predicted in linear cases, together with some decay estimates. We will illustrate this method with several explicit examples: Ekman layers, reflection of internal waves in a stratified fluid. . . We will also tackle semilinear problems, adding for instance a convection term to the previous examples. Eventually, we will introduce some tools for the study of the Prandtl equation.[-]

The purpose of these lectures is to present general methods to construct boundary layers both in linear and nonlinear contexts. We will explain how the boundary layer sizes and profiles can be predicted in linear cases, together with some decay estimates. We will illustrate this method with several explicit examples: Ekman layers, reflection of internal waves in a stratified fluid. . . We will also tackle semilinear problems, adding for instance ...[+]

35Q35 ; 35Q86 ; 76D10

Sélection Signaler une erreur

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

The purpose of these lectures is to present general methods to construct boundary layers both in linear and nonlinear contexts. We will explain how the boundary layer sizes and profiles can be predicted in linear cases, together with some decay estimates. We will illustrate this method with several explicit examples: Ekman layers, reflection of internal waves in a stratified fluid. . . We will also tackle semilinear problems, adding for instance a convection term to the previous examples. Eventually, we will introduce some tools for the study of the Prandtl equation.[-]

The purpose of these lectures is to present general methods to construct boundary layers both in linear and nonlinear contexts. We will explain how the boundary layer sizes and profiles can be predicted in linear cases, together with some decay estimates. We will illustrate this method with several explicit examples: Ekman layers, reflection of internal waves in a stratified fluid. . . We will also tackle semilinear problems, adding for instance ...[+]

35Q35 ; 35Q86 ; 76D10

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Documents Dalibard, Anne-Laure 8 résultats

Asymptotic methods for the study of oceanographic models - Lecture 1: model hierarchy - Dalibard, Anne-Laure (Auteur de la conférence) | CIRM H Nouveau

Asymptotic methods for the study of oceanographic models - Lecture 2: filtering methods - Dalibard, Anne-Laure (Auteur de la conférence) | CIRM H Nouveau

Asymptotic methods for the study of oceanographic models - Lecture 3: boundary layer methods - Dalibard, Anne-Laure (Auteur de la conférence) | CIRM H Nouveau

Stability of propagation fronts in congestion models - Dalibard, Anne-Laure (Auteur de la conférence) | CIRM H Nouveau

Boundary layer methods in fluid mechanics - Lecture 3 - Dalibard, Anne-Laure (Auteur de la conférence) | CIRM H Nouveau

Boundary layer methods in fluid mechanics - Lecture 2 - Dalibard, Anne-Laure (Auteur de la conférence) | CIRM H Nouveau

Boundary layer methods in fluid mechanics - Lecture 1 - Dalibard, Anne-Laure (Auteur de la conférence) | CIRM H Nouveau

Couches limites en mécanique des fluides - Dalibard, Anne-Laure (Auteur de la conférence) | CIRM Nouveau