Well-posedness of one-dimensional Korteweg models

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dc.contributor.authorBenzoni-Gavage, Sylvie
dc.contributor.authorDanchin, Raphael
dc.contributor.authorDescombes, Stephane
dc.date.accessioned2021-07-16T17:42:53Z
dc.date.available2021-07-16T17:42:53Z
dc.date.issued2006-05-02
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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent35 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationBenzoni-Gavage, S., Danchin, R., & Descombes, S. (2006). Well-posedness of one-dimensional Korteweg models. <i>Electronic Journal of Differential Equations, 2006</i>(59), pp. 1-35.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13932
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectCapillarity
dc.subjectKorteweg stress
dc.subjectLocal well-posedness
dc.subjectSchrodinger equation
dc.titleWell-posedness of one-dimensional Korteweg models
dc.typeArticle

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