Equations for Polymeric Materials

Masmoudi, Nader

doi:10.1007/978-3-319-13344-7_23

Cited by 7 publications

(1 citation statement)

References 66 publications

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“…In particular, we do not consider the perturbations that solve the governing equation only in the weak sense, although it is an important issue worth of further investigation. The reader interested in the discussion of the state-of-the-art rigorous mathematical theory of equations governing the motion of viscoelastic fluids is kindly referred to the discussion in Masmoudi (2018) or Barrett and Süli (2018).…”

Section: Concept Of Stabilitymentioning

confidence: 99%

Finite Amplitude Stability of Internal Steady Flows of the Giesekus Viscoelastic Rate-Type Fluid

Dostalík

Průša

Tůma

2019

Entropy

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We investigate the finite amplitude stability of internal steady flows of viscoelastic fluids described by the Giesekus model. The flow stability is investigated using a Lyapunov functional that is constructed on the basis of thermodynamical arguments. Using the functional, we derive bounds on the Reynolds and Weissenberg number that guarantee the unconditional asymptotic stability of the corresponding flow. Further, the functional allows one to explicitly analyse the role of elasticity in the onset of instability, which is a problem related to the elastic turbulence. The application of the theoretical results is documented in the finite amplitude stability analysis of Taylor-Couette flow of the Giesekus fluid.

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Section: Concept Of Stabilitymentioning

confidence: 99%

Finite Amplitude Stability of Internal Steady Flows of the Giesekus Viscoelastic Rate-Type Fluid

Dostalík

Průša

Tůma

2019

Entropy

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Global Well-Posedness of Strong Solutions of Doi Model with Large Viscous Stress

2019

J Nonlinear Sci

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We study models of dilute rigid rod-like polymer solutions. We establish the global wellposedness the Doi model for large data, and for arbitrarily large viscous stress parameter. The main ingredient in the proof is the fact that the viscous stress adds dissipation to high derivatives of velocity. * joonhyun@math.princeton.edu Notion of the solution. For the notion of solution, we follow the argument in [15]. By focusing on the evolution of macroscopic variables (trigonometric moments in this case), we can set up well-posedness of strong solutions for large class of initial data. In particular, higher regularity of Fokker-Planck equation is not necessary, and weak solution for Fokker-Planck equation is sufficient. On the other hand, since the effect of polymer to the flow are characterized by stresses, which are moments in (Doi), requiring spatial regularity for appropriate moments is necessary. In this regard, we introduce a terminology: for any n ∈ Z >0 , we let M n (x, t) := M I n (x, t) I:|I|=n := S 1 m I f (x, t, m)dm I:|I|=n (Moment)

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Global existence of classical solutions for a reactive polymeric fluid near equilibrium

Wang

Zhang

2022

Calc. Var.

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Equations for Polymeric Materials

Cited by 7 publications

References 66 publications

Finite Amplitude Stability of Internal Steady Flows of the Giesekus Viscoelastic Rate-Type Fluid

Finite Amplitude Stability of Internal Steady Flows of the Giesekus Viscoelastic Rate-Type Fluid

Global Well-Posedness of Strong Solutions of Doi Model with Large Viscous Stress

Global existence of classical solutions for a reactive polymeric fluid near equilibrium

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