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| HAL : hal-00686048, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Differential and integral equations 26, 3-4 (2013) 433-478 |
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| Planar traveling waves in capillary fluids |
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| Sylvie Benzoni-Gavage 1 |
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| (2013) |
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| By capillary fluids we mean compressible, inviscid fluids whose energy depends not only on their density but also on their density gradient. Their motion is thus governed by systems of conservation laws, either in Eulerian coordinates or in Lagrangian coordinates, that are higher order modification of the usual equations of gas dynamics. In both settings, we receive models that also arise in other fields, in particular in water waves theory and quantum hydrodynamics. Those Hamiltonian systems typically admit three types of planar traveling waves, namely, heteroclinic, homoclinic, and periodic ones. The purpose here is to review the main tools and results regarding the stability of those waves, under most general assumptions on the energy law. Special attention is devoted to the correspondence between traveling waves in Eulerian coordinates and those in Lagrangian coordinates. |
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| 1 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Lagrangian coordinates – kink – soliton – periodic wave – orbital stability – Boussinesq's moment of instability – Benjamin's impulse – Evans function – Krein signature – Whitham modulated equations. |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00686048, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00686048 | |
| oai:hal.archives-ouvertes.fr:hal-00686048 | |
| Contributeur : Sylvie Benzoni-Gavage | |
| Soumis le : Vendredi 6 Avril 2012, 18:02:49 | |
| Dernière modification le : Mardi 29 Janvier 2013, 08:02:20 | |
