Lagrangian methods for a general inhomogeneous incompressible Navier-Stokes-Korteweg system with variable capillarity and viscosity coefficients

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 is different from 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.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [26 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01390184
Contributor : Frederic Charve <>
Submitted on : Monday, October 31, 2016 - 10:10:47 PM
Last modification on : Friday, April 19, 2019 - 1:30:08 PM

Files

NSIK_Burtea_Charve.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

  • HAL Id : hal-01390184, version 1
  • ARXIV : 1611.00989

Citation

Cosmin Burtea, Frédéric Charve. Lagrangian methods for a general inhomogeneous incompressible Navier-Stokes-Korteweg system with variable capillarity and viscosity coefficients. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2017, 49 (5), pp.3476-3495. ⟨https://epubs.siam.org/doi/abs/10.1137/16M1101532⟩. ⟨hal-01390184⟩

Share

Metrics

Record views

197

Files downloads

89