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LAGRANGIAN METHODS FOR A GENERAL INHOMOGENEOUS INCOMPRESSIBLE NAVIERSTOKES-KORTEWEG SYSTEM WITH VARIABLE CAPILLARITY AND VISCOSITY COEFFICIENTS.

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Title: LAGRANGIAN METHODS FOR A GENERAL INHOMOGENEOUS INCOMPRESSIBLE NAVIERSTOKES-KORTEWEG SYSTEM WITH VARIABLE CAPILLARITY AND VISCOSITY COEFFICIENTS.
Authors: BURTEA, COSMIN1 cosmin.burtea@u-pec.fr, CHARVE, FRÉDÉRIC1 frederic.charve@u-pec.fr
Source: SIAM Journal on Mathematical Analysis. 2017, Vol. 49 Issue 5, p3476-3495. 20p.
Subjects: Incompressible flow, Navier-Stokes equations, Lagrange equations, Mathematical variables, Viscosity, Coefficients (Statistics)
Abstract: We study the inhomogeneous incompressible Navier--Stokes system endowed with a general capillary term. Thanks to recent methods based on Lagrangian change of variables, we obtain local well-posedness in critical Besov spaces (even if the integration index p ≠ 2) and for variable viscosity and capillary terms. In the case of constant coefficients and for initial data that are perturbations of a constant state, we are able to prove that the lifespan goes to infinity as the capillary coefficient goes to zero, connecting our result to the global existence result obtained by Danchin and Mucha for the incompressible Navier--Stokes system with constant coefficients. [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.)
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  Data: <searchLink fieldCode="DE" term="%22Incompressible+flow%22">Incompressible flow</searchLink><br /><searchLink fieldCode="DE" term="%22Navier-Stokes+equations%22">Navier-Stokes equations</searchLink><br /><searchLink fieldCode="DE" term="%22Lagrange+equations%22">Lagrange equations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+variables%22">Mathematical variables</searchLink><br /><searchLink fieldCode="DE" term="%22Viscosity%22">Viscosity</searchLink><br /><searchLink fieldCode="DE" term="%22Coefficients+%28Statistics%29%22">Coefficients (Statistics)</searchLink>
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  Data: We study the inhomogeneous incompressible Navier--Stokes system endowed with a general capillary term. Thanks to recent methods based on Lagrangian change of variables, we obtain local well-posedness in critical Besov spaces (even if the integration index p ≠ 2) and for variable viscosity and capillary terms. In the case of constant coefficients and for initial data that are perturbations of a constant state, we are able to prove that the lifespan goes to infinity as the capillary coefficient goes to zero, connecting our result to the global existence result obtained by Danchin and Mucha for the incompressible Navier--Stokes system with constant coefficients. [ABSTRACT FROM AUTHOR]
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  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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        Value: 10.1137/16M1101532
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      – Code: eng
        Text: English
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        PageCount: 20
        StartPage: 3476
    Subjects:
      – SubjectFull: Incompressible flow
        Type: general
      – SubjectFull: Navier-Stokes equations
        Type: general
      – SubjectFull: Lagrange equations
        Type: general
      – SubjectFull: Mathematical variables
        Type: general
      – SubjectFull: Viscosity
        Type: general
      – SubjectFull: Coefficients (Statistics)
        Type: general
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      – TitleFull: LAGRANGIAN METHODS FOR A GENERAL INHOMOGENEOUS INCOMPRESSIBLE NAVIERSTOKES-KORTEWEG SYSTEM WITH VARIABLE CAPILLARITY AND VISCOSITY COEFFICIENTS.
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              M: 11
              Text: 2017
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