VANISHING CAPILLARITY LIMIT OF THE NAVIER--STOKES--KORTEWEG SYSTEM IN ONE DIMENSION WITH DEGENERATE VISCOSITY COEFFICIENT AND DISCONTINUOUS INITIAL DENSITY.
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| Title: | VANISHING CAPILLARITY LIMIT OF THE NAVIER--STOKES--KORTEWEG SYSTEM IN ONE DIMENSION WITH DEGENERATE VISCOSITY COEFFICIENT AND DISCONTINUOUS INITIAL DENSITY. |
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| Authors: | BURTEA, COSMIN1 cosmin.burtea@imj-prg.fr, HASPOT, BORIS2 haspot@ceremade.dauphine.fr |
| Source: | SIAM Journal on Mathematical Analysis. 2022, Vol. 54 Issue 2, p1428-1469. 42p. |
| Subjects: | Discontinuous coefficients, Capillarity, Viscosity, Density, Fluid mechanics, Stokes flow |
| Abstract: | In the first main result of this paper we prove that one can approximate discontinious solutions of the 1d Navier Stokes system with solutions of the 1d Navier-Stokes-Korteweg system as the capilarity parameter tends to 0. Moreover, we allow the viscosity coefficients μ = μ (ρ) to degenerate near vaccum. In order to obtain this result, we propose two main technical novelties. First of all, we provide an upper bound for the density verifing NSK that does not degenerate when the capillarity coefficient tends to 0. Second of all, we are able to show that the positive part of the effective velocity is bounded uniformly w.r. t. the capillary coefficient. This turns out to be crucial in providing a lower bound for the density. The second main result states the existene of unique finite-energy global strong solutions for the 1d Navier-Stokes system assuming only that ρ0, 1/ρ0 ∈ L ∞. This last result finds itself a natural application in the context of the mathematical modeling of multiphase flows. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 155990063 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: VANISHING CAPILLARITY LIMIT OF THE NAVIER--STOKES--KORTEWEG SYSTEM IN ONE DIMENSION WITH DEGENERATE VISCOSITY COEFFICIENT AND DISCONTINUOUS INITIAL DENSITY. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22BURTEA%2C+COSMIN%22">BURTEA, COSMIN</searchLink><relatesTo>1</relatesTo><i> cosmin.burtea@imj-prg.fr</i><br /><searchLink fieldCode="AR" term="%22HASPOT%2C+BORIS%22">HASPOT, BORIS</searchLink><relatesTo>2</relatesTo><i> haspot@ceremade.dauphine.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Mathematical+Analysis%22">SIAM Journal on Mathematical Analysis</searchLink>. 2022, Vol. 54 Issue 2, p1428-1469. 42p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Discontinuous+coefficients%22">Discontinuous coefficients</searchLink><br /><searchLink fieldCode="DE" term="%22Capillarity%22">Capillarity</searchLink><br /><searchLink fieldCode="DE" term="%22Viscosity%22">Viscosity</searchLink><br /><searchLink fieldCode="DE" term="%22Density%22">Density</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+mechanics%22">Fluid mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Stokes+flow%22">Stokes flow</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the first main result of this paper we prove that one can approximate discontinious solutions of the 1d Navier Stokes system with solutions of the 1d Navier-Stokes-Korteweg system as the capilarity parameter tends to 0. Moreover, we allow the viscosity coefficients μ = μ (ρ) to degenerate near vaccum. In order to obtain this result, we propose two main technical novelties. First of all, we provide an upper bound for the density verifing NSK that does not degenerate when the capillarity coefficient tends to 0. Second of all, we are able to show that the positive part of the effective velocity is bounded uniformly w.r. t. the capillary coefficient. This turns out to be crucial in providing a lower bound for the density. The second main result states the existene of unique finite-energy global strong solutions for the 1d Navier-Stokes system assuming only that ρ0, 1/ρ0 ∈ L ∞. This last result finds itself a natural application in the context of the mathematical modeling of multiphase flows. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/21M1428686 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 42 StartPage: 1428 Subjects: – SubjectFull: Discontinuous coefficients Type: general – SubjectFull: Capillarity Type: general – SubjectFull: Viscosity Type: general – SubjectFull: Density Type: general – SubjectFull: Fluid mechanics Type: general – SubjectFull: Stokes flow Type: general Titles: – TitleFull: VANISHING CAPILLARITY LIMIT OF THE NAVIER--STOKES--KORTEWEG SYSTEM IN ONE DIMENSION WITH DEGENERATE VISCOSITY COEFFICIENT AND DISCONTINUOUS INITIAL DENSITY. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: BURTEA, COSMIN – PersonEntity: Name: NameFull: HASPOT, BORIS IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: 2022 Type: published Y: 2022 Identifiers: – Type: issn-print Value: 00361410 Numbering: – Type: volume Value: 54 – Type: issue Value: 2 Titles: – TitleFull: SIAM Journal on Mathematical Analysis Type: main |
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