EXISTENCE OF WEAK SOLUTIONS FOR PARTICLE-LADEN FLOW WITH SURFACE TENSION

被引：0

作者：

Taranets, Roman M. ^{[1
,2
,3
]}

Wong, Jeffrey T. ^{[2
,4
]}

机构：

[1] NASU, Inst Appl Math & Mech, 1 Dobrovolskogo Str, UA-84100 Sloviansk, Ukraine

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[3] VasylStus Donetsk Natl Univ, 21,600 Richya Str, UA-21021 Vinnytsia, Ukraine

[4] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 10期

关键词：

Fourth-order degenerate parabolic equations; existence of weak solutions; thin liquid films; suspensions; multiphase flows; THIN VISCOUS FILMS; LIQUID-FILMS; NONNEGATIVE SOLUTIONS; EQUATIONS; DYNAMICS; APPROXIMATION; RESUSPENSION; CONVECTION; EVOLUTION; SYSTEMS;

D O I：

10.3934/dcds.2018217

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of solutions for a coupled system modeling the flow of a suspension of fluid and negatively buoyant non-colloidal particles in the thin film limit. The equations take the form of a fourth-order nonlinear degenerate parabolic equation for the film height h coupled to a second-order degenerate parabolic equation for the particle density psi. We prove the existence of physically relevant solutions, which satisfy the uniform bounds 0 <= psi/h <= 1 and h >= 0.

引用

页码：4979 / 4996

页数：18

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