GLOBAL EXISTENCE RESULT FOR THE GENERALIZED PETERLIN VISCOELASTIC MODEL

被引：27

作者：

Lukacova-Medvidova, Maria ^{[1
]}

Mizerova, Hana ^{[1
]}

Necasova, Sarka ^{[2
]}

Renardy, Michael ^{[3
]}

机构：

[1] Johannes Gutenberg Univ Mainz, Inst Math, D-55128 Mainz, Germany

[2] CAS, Inst Math, Zitna 25, Prague 11567 1, Czech Republic

[3] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2017年 / 49卷 / 04期

基金：

美国国家科学基金会;

关键词：

Peterlin viscoelastic equations; global existence; weak solutions; strong solutions; MICRO-MACRO MODEL; POLYMERIC FLUID; WELL-POSEDNESS; WEAK SOLUTIONS; DILUTE POLYMERS; KINETIC-MODELS; OLDROYD-B; EQUATIONS; APPROXIMATION; HYDRODYNAMICS;

D O I：

10.1137/16M1068505

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a class of differential models of viscoelastic fluids with diffusive stress. These constitutive models are motivated by Peterlin dumbbell theories with a nonlinear spring law for an infinitely extensible spring. A diffusion term is included in the constitutive model. Under appropriate assumptions on the nonlinear constitutive functions, we prove global existence of weak solutions for large data. For creeping flows and two-dimensional flows, we prove the global existence of a classical solution under stronger assumptions.

引用

页码：2950 / 2964

页数：15

共 41 条

[1]

[Anonymous], 2015, DISSERTATION

[2] Existence of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers with variable density and viscosity [J].

Barrett, John W. ;

Sueli, Endre .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (12) :3610-3677

[3] FINITE ELEMENT APPROXIMATION OF FINITELY EXTENSIBLE NONLINEAR ELASTIC DUMBBELL MODELS FOR DILUTE POLYMERS [J].

Barrett, John W. ;

Sueli, Endre .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2012, 46 (04) :949-978

[4] EXISTENCE AND APPROXIMATION OF A (REGULARIZED) OLDROYD-B MODEL [J].

Barrett, John W. ;

Boyaval, Sebastien .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2011, 21 (09) :1783-1837

[5] EXISTENCE AND EQUILIBRATION OF GLOBAL WEAK SOLUTIONS TO KINETIC MODELS FOR DILUTE POLYMERS I: FINITELY EXTENSIBLE NONLINEAR BEAD-SPRING CHAINS [J].

Barrett, John W. ;

Sueli, Endre .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2011, 21 (06) :1211-1289

[6]

Bird R. Byron, 1987, Kinetic theory, V2

[7]

Bris C.L., 2009, Multiscale Modelling of Complex Fluids: A Mathematical Initiation, P49, DOI DOI 10.1007/978-3-540-88857-42

[8] CREEPING FLOW OF DILUTE POLYMER-SOLUTIONS PAST CYLINDERS AND SPHERES [J].

CHILCOTT, MD ;

RALLISON, JM .

JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 1988, 29 (1-3) :381-432

[9] Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D [J].

Constantin, P. ;

Masmoudi, Nader .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 278 (01) :179-191

[10] Note on Global Regularity for Two-Dimensional Oldroyd-B Fluids with Diffusive Stress [J].

Constantin, Peter ;

Kliegl, Markus .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2012, 206 (03) :725-740

← 1 2 3 4 5 →