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EDP SCIENCES Introduction aux équations de Navier-Stokes incompressibles

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Description

Dans la modélisation mathématique de l'hydrodynamique, les équations de Navier-Stokes sont des équations aux dérivées partielles non linéaires qui décrivent l'écoulement de certains fluides. D'un point de vue purement mathématique, ces équations soulèvent des problèmes passionnants qui sont pour la plupart entièrement ouverts et qui font l'objet de recherches actuelles très actives. Issu d'un cours de Master 2 donné à l'Université Paris-Saclay, ce livre est une introduction destinée à donner les outils de base pour comprendre l'étude mathématique de ces équations. Le premier chapitre propose une rapide déduction physique de ces équations tandis que le deuxième chapitre introduit le cadre mathématique qui sera utilisé par la suite. Plusieurs types de solutions des équations de Navier-Stokes sont alors abordés : les solutions classiques dans le chapitre 3, les solutions de type mild dans les chapitres 4 et 5 et enfin les solutions faibles dans les chapitres 6 et 7. Des problèmes d'explosion, de régularité et d'unicité pour les équations stationnaires sont également étudiés. Chaque chapitre se termine par des exercices qui proposent des compléments utiles ainsi quelques développements inspirés d'articles de recherche récents.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
23 January 2025
Listed Since
09 August 2024

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