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dc.contributor.authorBenzoni-Gavage, Sylvie ( )
dc.contributor.authorDanchin, Raphael ( Orcid Icon 0000-0003-3072-3341 )
dc.contributor.authorDescombes, Stephane ( )
dc.date.accessioned2021-07-16T17:42:53Z
dc.date.available2021-07-16T17:42:53Z
dc.date.issued2006-05-02
dc.identifier.citationBenzoni-Gavage, S., Danchin, R., & Descombes, S. (2006). Well-posedness of one-dimensional Korteweg models. Electronic Journal of Differential Equations, 2006(59), pp. 1-35.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13932
dc.description.abstractWe investigate the initial-value problem for one-dimensional compressible fluids endowed with internal capillarity. We focus on the isothermal inviscid case with variable capillarity. The resulting equations for the density and the velocity, consisting of the mass conservation law and the momentum conservation with Korteweg stress, are a system of third order nonlinear dispersive partial differential equations. Additionally, this system is Hamiltonian and admits travelling solutions, representing propagating phase boundaries with internal structure. By change of unknown, it roughly reduces to a quasilinear Schrodinger equation. This new formulation enables us to prove local well-posedness for smooth perturbations of travelling profiles and almost-global existence for small enough perturbations. A blow-up criterion is also derived.en_US
dc.formatText
dc.format.extent35 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.source.uriElectronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectCapillarityen_US
dc.subjectKorteweg stressen_US
dc.subjectLocal well-posednessen_US
dc.subjectSchrodinger equationen_US
dc.titleWell-posedness of one-dimensional Korteweg modelsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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