Continuity of Velocity Gradients in Suspensions of Rod–like Molecules

Otto, Félix; Tzavaras, Athanasios E.

doi:10.1007/s00220-007-0373-5

Cited by 82 publications

(71 citation statements)

References 10 publications

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“…For the Doi model, we do not need to make the co-rotational simplification since we do not have the potential singularity as in the FENE model. We refer to [13], [4] and [5] for previous results.…”

Section: The Doi Modelmentioning

confidence: 99%

Global existence of weak solutions to some micro-macro models

Lions

Masmoudi

2007

Comptes Rendus. Mathématique

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We prove global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we take a sequence of weak solutions which converges weakly and such that the initial data converges strongly then the weak limit is also a solution.To cite this article: A. Name1, A. Name2, C. R. Acad. Sci. Paris, Ser. I 340 (2005).Key words Fokker-Planck equations, Navier-Stokes equations, FENE model, Doi model, global solutions. AMS subject classification 35Q30, 82C31, 76A05. RésuméExistence globale de solutions faibles a quelques modèles micro-macro On montre l'existence globale de solutions faiblesà certains modèles micro-macro. En particulier onétudie le modèle FENE (le cas des ressorts) et le modèle de Doi (le cas des barres rigides) La preuve est basée sur la propagation de la compacité.Pour citer cet article : A. Name1, A. Name2, C. R. Acad. Sci. Paris, Ser. I 340 (2005).Version française abrégée Le modèle FENEOn montre l'existence globale de solutions faibles au modèle FENE où les polymères sont considérés comme des ressorts avec uneélongation finie. Le systéme est donné par (voir la version anglaise pour les notations).Email addresses: lions@ens.fr (P.-L. Lions), masmoudi@cims.nyu.edu (Nader Masmoudi). Preprint submitted to Elsevier Science 2 mai 2007(1) Le modèle de Doi ou modèle rigideDans le modèle de Doi, les polymères sont représentés par des barres rigides l'orientation R.On démontre le théorème suivant

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Section: The Doi Modelmentioning

confidence: 99%

Global existence of weak solutions to some micro-macro models

Lions

Masmoudi

2007

Comptes Rendus. Mathématique

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“…PDE models include non-Newtonian viscoelastic models like the Oldroyd-B equations, tensor models, and kinetic models, in which Navier-Stokes equations are coupled to linear or nonlinear Fokker-Planck equations. The well-posedness theory is difficult even in two space dimensions, and consequently the mathematical theory of complex fluids is in its developing stages ( [43], [48], [52], [76], [89], [98], [100], [101], [103], [115]). Some of the models of complex fluids involve stochastic PDEs, or hybrid systems, in which PDEs are coupled to stochastic differential equations.…”

Section: Introductionmentioning

confidence: 99%

On the Euler equations of incompressible fluids

Constantin

2007

Bull. Amer. Math. Soc.

209

212

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Abstract. Euler equations of incompressible fluids use and enrich many branches of mathematics, from integrable systems to geometric analysis. They present important open physical and mathematical problems. Examples include the stable statistical behavior of ill-posed free surface problems such as the Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The paper describes some of the open problems related to the incompressible Euler equations, with emphasis on the blowup problem, the inviscid limit and anomalous dissipation. Some of the recent results on the quasigeostrophic model are also mentioned.

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“…Indeed, a principle based on an energy dissipation balance was proposed in [7], where the regularity of nonlinear Fokker-Planck systems coupled with Stokes equations in 3D was also proved. In particular the Doi model (or Rigid model) was considered in [29] where the linear Fokker-Planck system is coupled with a stationary Stokes equations. The nonlinear Fokker-Planck equation driven by a time averaged Navier-Stokes system in 2D was studied in [8].…”

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confidence: 99%