American Institute of Mathematical Sciences

Advanced
June  2010, 3(2): 311-324. doi: 10.3934/dcdss.2010.3.311

On the local strong solutions for the FENE dumbbell model

Ondřej Kreml 1, and  Milan Pokorný 1,

1. 

Mathematical Institute of Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic, Czech Republic

Received  March 2009 Revised  June 2009 Published  April 2010

We consider a model for the polymeric fluid which has recently been studied in [12]. We show the local-in-time existence of a strong solution to the corresponding system of partial differential equations under less regularity assumptions on the initial data than in the mentioned paper. The main difference in our approach is the use of the $L^p$ theory for the Stokes system.
Keywords: Viscoelastic fluid, $L^p$ theory., polymeric fluid, Oldroyd model, local strong solution.
Mathematics Subject Classification: Primary: 35Q35, 76D03; Secondary: 35Q3.
Citation: Ondřej Kreml, Milan Pokorný. On the local strong solutions for the FENE dumbbell model. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 311-324. doi: 10.3934/dcdss.2010.3.311
[1]

Kun Wang, Yangping Lin, Yinnian He. Asymptotic analysis of the equations of motion for viscoelastic oldroyd fluid. Discrete & Continuous Dynamical Systems - A, 2012, 32 (2) : 657-677. doi: 10.3934/dcds.2012.32.657
[2]

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
[3]

A. Jiménez-Casas, Mario Castro, Justine Yassapan. Finite-dimensional behavior in a thermosyphon with a viscoelastic fluid. Conference Publications, 2013, 2013 (special) : 375-384. doi: 10.3934/proc.2013.2013.375
[4]

Martina Bukač, Sunčica Čanić. Longitudinal displacement in viscoelastic arteries: A novel fluid-structure interaction computational model, and experimental validation. Mathematical Biosciences & Engineering, 2013, 10 (2) : 295-318. doi: 10.3934/mbe.2013.10.295
[5]

Hugo Beirão da Veiga. Turbulence models, $p-$fluid flows, and $W^{2, L}$ regularity of solutions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 769-783. doi: 10.3934/cpaa.2009.8.769
[6]

Matthias Hieber, Miho Murata. The $L^p$-approach to the fluid-rigid body interaction problem for compressible fluids. Evolution Equations & Control Theory, 2015, 4 (1) : 69-87. doi: 10.3934/eect.2015.4.69
[7]

Hiroshi Inoue, Kei Matsuura, Mitsuharu Ôtani. Strong solutions of magneto-micropolar fluid equation. Conference Publications, 2003, 2003 (Special) : 439-448. doi: 10.3934/proc.2003.2003.439
[8]

Fabio Cipriani, Gabriele Grillo. On the $l^p$ -agmon's theory. Conference Publications, 1998, 1998 (Special) : 167-176. doi: 10.3934/proc.1998.1998.167
[9]

Yaqing Liu, Liancun Zheng. Second-order slip flow of a generalized Oldroyd-B fluid through porous medium. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2031-2046. doi: 10.3934/dcdss.2016083
[10]

Kun Wang, Yinnian He, Yueqiang Shang. Fully discrete finite element method for the viscoelastic fluid motion equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 665-684. doi: 10.3934/dcdsb.2010.13.665
[11]

Victor Zvyagin, Vladimir Orlov. On one problem of viscoelastic fluid dynamics with memory on an infinite time interval. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3855-3877. doi: 10.3934/dcdsb.2018114
[12]

Eduard Feireisl, Šárka Nečasová, Reimund Rautmann, Werner Varnhorn. New developments in mathematical theory of fluid mechanics. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : i-ii. doi: 10.3934/dcdss.2014.7.5i
[13]

Chunhua Jin. Global classical solution and stability to a coupled chemotaxis-fluid model with logistic source. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3547-3566. doi: 10.3934/dcds.2018150
[14]

Ciro D'Apice, Rosanna Manzo. A fluid dynamic model for supply chains. Networks & Heterogeneous Media, 2006, 1 (3) : 379-398. doi: 10.3934/nhm.2006.1.379
[15]

Youcef Amirat, Kamel Hamdache. On a heated incompressible magnetic fluid model. Communications on Pure & Applied Analysis, 2012, 11 (2) : 675-696. doi: 10.3934/cpaa.2012.11.675
[16]

Jean-Jérôme Casanova. Existence of time-periodic strong solutions to a fluid–structure system. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3291-3313. doi: 10.3934/dcds.2019136
[17]

Cung The Anh, Vu Manh Toi. Local exact controllability to trajectories of the magneto-micropolar fluid equations. Evolution Equations & Control Theory, 2017, 6 (3) : 357-379. doi: 10.3934/eect.2017019
[18]

Lingbing He. On the global smooth solution to 2-D fluid/particle system. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 237-263. doi: 10.3934/dcds.2010.27.237
[19]

Ruizhao Zi. Global solution in critical spaces to the compressible Oldroyd-B model with non-small coupling parameter. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6437-6470. doi: 10.3934/dcds.2017279
[20]

I. D. Chueshov, Iryna Ryzhkova. A global attractor for a fluid--plate interaction model. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1635-1656. doi: 10.3934/cpaa.2013.12.1635

2018 Impact Factor: 0.545

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences