You can manage bookmarks using lists, please log in to your user account for this.
Media type:
E-Article
Title:
From Vlasov Equation to Degenerate Nonlocal Cahn-Hilliard Equation
Contributor:
Elbar, Charles;
Mason, Marco;
Perthame, Benoît;
Skrzeczkowski, Jakub
imprint:
Springer Science and Business Media LLC, 2023
Published in:Communications in Mathematical Physics
Language:
English
DOI:
10.1007/s00220-023-04663-3
ISSN:
0010-3616;
1432-0916
Origination:
Footnote:
Description:
<jats:title>Abstract</jats:title><jats:p>We provide a rigorous mathematical framework to establish the hydrodynamic limit of the Vlasov model introduced in Takata and Noguchi (J. Stat. Phys. 172:880-903, 2018) by Noguchi and Takata in order to describe phase transition of fluids by kinetic equations. We prove that, when the scale parameter tends to 0, this model converges to a nonlocal Cahn-Hilliard equation with degenerate mobility. For our analysis, we introduce apropriate forms of the short and long range potentials which allow us to derive Helmhotlz free energy estimates. Several compactness properties follow from the energy, the energy dissipation and kinetic averaging lemmas. In particular we prove a new weak compactness bound on the flux.</jats:p>