Global Solutions to the Oldroyd-B Model with a Class of Large Initial Data

Fang, Daoyuan; Zi, Ruizhao

doi:10.1137/15m1037020

Cited by 60 publications

(21 citation statements)

References 34 publications

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“…The similar results were obtained in several papers by virtue of different methods, see Z. Lei and Y. Zhou [19], Z. Lei, C. Liu and Y. Zhou [18], T. Zhang and D. Fang [29], Y. Zhu [30]. D. Fang, M. Hieber and R. Zi proved the global existence of strong solutions with a class of large data [12,13].…”

Section: Introductionsupporting

confidence: 84%

Global well-posedness for the Phan-Thein-Tanner model in critical Besov spaces without damping

Chen

Luo

Zhai

2019

Journal of Mathematical Physics

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In this paper, we mainly investigate the Cauchy problem for the Phan-Thein- Tanner (PTT) model. The PPT model can be viewed as a Navier-Stokes equations couple with a nonlinear transport system. This model is derived from network theory for the polymeric fluid. We study about the global well posedness of the PTT model in critical Besov spaces. When the initial data is a small perturbation over around the equilibrium, we prove that the strong solution in critical Besov spaces exists globally. 2010 AMS Classification: 35A01, 35B45, 35Q35, 76A05, 76D03.

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Section: Introductionsupporting

confidence: 84%

Global well-posedness for the Phan-Thein-Tanner model in critical Besov spaces without damping

Chen

Luo

Zhai

2019

Journal of Mathematical Physics

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“…Starting with the pioneering works of Renardy [35] and Guillopé & Saut [20], mathematical models of viscoelastic fluids of Oldroyd type have been studied by many authors. We mention here only the papers [2,3,5,9,10,12,13,14,15,16,17,18,21,22,26,28,30,39,40,41]. A detailed analysis of different problems and results related to the Oldroyd model and other similar non-Newtonian models can be found in the review article [37].…”

Section: Remarkmentioning

confidence: 99%

Steady flows of an Oldroyd fluid with threshold slip

Baranovskii¹

2019

Communications on Pure &Amp; Applied Analysis

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We consider a mathematical model that describes 3D steady flows of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain under mixed boundary conditions, including a threshold-slip boundary condition. Using the concept of weak solutions, we reduce the original slip problem to a coupled system of variational inequalities and equations for the velocity field and stresses. For arbitrary large data (forcing and boundary data) and suitable material constants, we prove the existence of weak solutions and establish some of their properties.

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“…Chemin and Masmoudi [7] initiated the study of the global existence and uniqueness in the critical Besov spaces, and their results were improved later by Zi, Fang and Zhang [16] to the case of the non-small coupling parameter. For more results on the well-posedness and the blow-up criterion, one refers to [7,8,16,17,22] and references therein. Now let us say a few words about the so-called critical spaces, for the incompressible Navier-Stokes equations…”

Section: Introductionmentioning

confidence: 99%

Global Well-Posedness in the Critical Besov Spaces for the Incompressible Oldroyd-B Model Without Damping Mechanism

Chen

Hao

2019

J. Math. Fluid Mech.

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We prove the global well-posedness in the critical Besov spaces for the incompressible Oldroyd-B model without damping mechanism on the stress tensor in R d for the small initial data. Our proof is based on the observation that the behaviors of Green's matrix to the system of u, (−∆) − 1 2 P∇ · τ as well as the effects of τ change from the low frequencies to the high frequencies and the construction of the appropriate energies in different frequencies.

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Global Solutions to the Oldroyd-B Model with a Class of Large Initial Data

Cited by 60 publications

References 34 publications

Global well-posedness for the Phan-Thein-Tanner model in critical Besov spaces without damping

Global well-posedness for the Phan-Thein-Tanner model in critical Besov spaces without damping

Steady flows of an Oldroyd fluid with threshold slip

Global Well-Posedness in the Critical Besov Spaces for the Incompressible Oldroyd-B Model Without Damping Mechanism

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