American Institute of Mathematical Sciences

Advanced
March  2005, 4(1): 23-43. doi: 10.3934/cpaa.2005.4.23

Existence of steady flows of slightly compressible viscoelastic fluids of White-Metzner type around an obstacle

Colette Guillopé 1, , Abdelilah Hakim 2, and  Raafat Talhouk 3,

1. 

Laboratoire d'Analyse et de Mathématiques appliquées, CNRS et Université Paris XII -- Val de Marne, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
2. 

Mathématiques, Faculté des Sciences et Techniques de Guéliz, B.P. 549, Avenue Abdelkrim Elkhattabi, Marrakech, Morocco
3. 

Mathématiques, Faculté des Sciences Section 1, Université libanaise, Beyrouth, Lebanon

Received  April 2003 Revised  March 2004 Published  December 2004

This work is concerned with the study of steady flows, around an obstacle, of slightly compressible viscoelastic fluids, for which the extra-stress tensor is given by a White-Metzner constitutive law. The existence and uniqueness of such flows are shown, when Newtonian viscosity is present (Jeffreys' model), and for small data.
Keywords: Viscoelastic fluids, flows around obstacles., White-Metzner model, weak compressibility, steady flows.
Mathematics Subject Classification: 76D03, 35B10, 35B3.
Citation: Colette Guillopé, Abdelilah Hakim, Raafat Talhouk. Existence of steady flows of slightly compressible viscoelastic fluids of White-Metzner type around an obstacle. Communications on Pure & Applied Analysis, 2005, 4 (1) : 23-43. doi: 10.3934/cpaa.2005.4.23
[1]

Colette Guillopé, Zaynab Salloum, Raafat Talhouk. Regular flows of weakly compressible viscoelastic fluids and the incompressible limit. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1001-1028. doi: 10.3934/dcdsb.2010.14.1001
[2]

Allen Montz, Hamid Bellout, Frederick Bloom. Existence and uniqueness of steady flows of nonlinear bipolar viscous fluids in a cylinder. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2107-2128. doi: 10.3934/dcdsb.2015.20.2107
[3]

Jinqiao Duan, Vincent J. Ervin, Daniel Schertzer. Dispersion in flows with obstacles and uncertainty. Conference Publications, 2001, 2001 (Special) : 131-136. doi: 10.3934/proc.2001.2001.131
[4]

Wenjing Zhao. Weak-strong uniqueness of incompressible magneto-viscoelastic flows. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2907-2917. doi: 10.3934/cpaa.2020127
[5]

W. Wei, Yin Li, Zheng-An Yao. Decay of the compressible viscoelastic flows. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1603-1624. doi: 10.3934/cpaa.2016004
[6]

Zaynab Salloum. Flows of weakly compressible viscoelastic fluids through a regular bounded domain with inflow-outflow boundary conditions. Communications on Pure & Applied Analysis, 2010, 9 (3) : 625-642. doi: 10.3934/cpaa.2010.9.625
[7]

M. Bulíček, P. Kaplický. Incompressible fluids with shear rate and pressure dependent viscosity: Regularity of steady planar flows. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 41-50. doi: 10.3934/dcdss.2008.1.41
[8]

Xianpeng Hu, Hao Wu. Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows. Discrete & Continuous Dynamical Systems - A, 2015, 35 (8) : 3437-3461. doi: 10.3934/dcds.2015.35.3437
[9]

Michael Cranston, Benjamin Gess, Michael Scheutzow. Weak synchronization for isotropic flows. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3003-3014. doi: 10.3934/dcdsb.2016084
[10]

Michela Eleuteri, Elisabetta Rocca, Giulio Schimperna. On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2497-2522. doi: 10.3934/dcds.2015.35.2497
[11]

Evgenii S. Baranovskii. Steady flows of an Oldroyd fluid with threshold slip. Communications on Pure & Applied Analysis, 2019, 18 (2) : 735-750. doi: 10.3934/cpaa.2019036
[12]

Kun Wang, Yinnian He, Yanping Lin. Long time numerical stability and asymptotic analysis for the viscoelastic Oldroyd flows. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1551-1573. doi: 10.3934/dcdsb.2012.17.1551
[13]

Xianpeng Hu, Dehua Wang. The initial-boundary value problem for the compressible viscoelastic flows. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 917-934. doi: 10.3934/dcds.2015.35.917
[14]

Charles Amorim, Miguel Loayza, Marko A. Rojas-Medar. The nonstationary flows of micropolar fluids with thermal convection: An iterative approach. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020193
[15]

Aneta Wróblewska-Kamińska. Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (6) : 2565-2592. doi: 10.3934/dcds.2013.33.2565
[16]

Paul Deuring, Stanislav Kračmar, Šárka Nečasová. A representation formula for linearized stationary incompressible viscous flows around rotating and translating bodies. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 237-253. doi: 10.3934/dcdss.2010.3.237
[17]

Isaac A. García, Jaume Giné, Susanna Maza. Linearization of smooth planar vector fields around singular points via commuting flows. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1415-1428. doi: 10.3934/cpaa.2008.7.1415
[18]

Eduard Feireisl. On weak solutions to a diffuse interface model of a binary mixture of compressible fluids. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 173-183. doi: 10.3934/dcdss.2016.9.173
[19]

Daoyuan Fang, Ting Zhang, Ruizhao Zi. Dispersive effects of the incompressible viscoelastic fluids. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 5261-5295. doi: 10.3934/dcds.2018233
[20]

Youcef Amirat, Laurent Chupin, Rachid Touzani. Weak solutions to the equations of stationary magnetohydrodynamic flows in porous media. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2445-2464. doi: 10.3934/cpaa.2014.13.2445

2019 Impact Factor: 1.105

Tools

Metrics

  • PDF downloads (32)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences