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

La, Joonhyun

doi:10.1007/s00332-019-09533-8

Cited by 10 publications

(4 citation statements)

References 20 publications

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“…Existence of global weak entropy solution for this generalization of the Doi model is studied in [CL13] All the previously mentioned papers neglect the presence of the additional viscous stress σ v , i.e., they pretend σ = σ e . Global well-posedness for the Doi model including the full viscoelastic stress σ is treated in [LM07; ZZ08;La19].…”

Section: Previous Mathematical Resultsmentioning

confidence: 99%

Derivation of the viscoelastic stress in Stokes flows induced by non-spherical Brownian rigid particles through homogenization

Höfer¹,

Leocata²,

Mecherbet³

2022

Preprint

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We consider a microscopic model of n identical axis-symmetric rigid Brownian particles suspended in a Stokes flow. We rigorously derive in the homogenization limit of many small particles a classical formula for the viscoelastic stress that appears in so-called Doi models which couple a Fokker-Planck equation to the Stokes equations. We consider both Deborah numbers of order 1 and very small Deborah numbers. Our microscopic model contains several simplifications, most importantly, we neglect the time evolution of the particle centers as well as hydrodynamic interaction for the evolution of the particle orientations.The microscopic fluid velocity is modeled by the Stokes equations with given torques at the particles in terms of Stratonovitch noise. We give a meaning to this PDE in terms of an infinite dimensional Stratonovitch integral. This requires the analysis of the shape derivatives of the Stokes equations in perforated domains, which we accomplish by the method of reflections.

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Section: Previous Mathematical Resultsmentioning

confidence: 99%

Derivation of the viscoelastic stress in Stokes flows induced by non-spherical Brownian rigid particles through homogenization

Höfer¹,

Leocata²,

Mecherbet³

2022

Preprint

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“…This model recently has been studied intensively. See [3] for a list of known results of the Doi models. But, to the best of our knowledge, our paper is the first mathematical work dealing with passive and active models.…”

Section: Final Remarkmentioning

confidence: 99%

Global existence of solutions to some equations modeling phase separation of self-propelled particles

Bae

2020

SN Partial Differ. Equ. Appl.

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In this paper, we provide mathematical results on some models of phase separation of selfpropelled particles. To this end, we first introduce a general model presented in Tiribocchi et al. (Phys Rev Lett 115:188302, 2015). We then proceed to handle some particular cases where k, whose role is to violate time reversal symmetry, is zero (passive) or nonzero (active). We also cover some models coupled with incompressible fluids.

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“…In the second class of models (sometimes called Doi-type), to which the system (1.1)-(1.3) belongs, the immersed polymers are treated as rigid rods. The many existence and uniqueness results for this class of models include [3,14,16,17,18,32,35,38,41,49,53,58]. Note that no swimming is included in these previous results.…”

Section: Introductionmentioning

confidence: 97%

On the stabilizing effect of swimming in an active suspension

Albritton¹,

Ohm²

2022

Preprint

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We consider a kinetic model of an active suspension of rod-like microswimmers. In certain regimes, swimming has a stabilizing effect on the suspension. We quantify this effect near homogeneous isotropic equilibria ψ = const. Notably, in the absence of particle (translational and orientational) diffusion, swimming is the only stabilizing mechanism. On the torus, in the non-diffusive regime, we demonstrate linear Landau damping up to the stability threshold predicted in the applied literature. With small diffusion, we demonstrate nonlinear stability of arbitrary equilibrium values for pullers (rear-actuated swimmers) and enhanced dissipation for both pullers and pushers (front-actuated swimmers) at small concentrations. On the whole space, we prove nonlinear stability of the vacuum equilibrium due to generalized Taylor dispersion. Contents 1. Introduction 1 2. Landau damping 9 3. Taylor dispersion 15 4. Enhanced dissipation 23 Appendix A. Nondimensionalization 32 Appendix B. Strong solution theory 33 Appendix C. Proof of Lemma 4.3 36 References 37

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

Cited by 10 publications

References 20 publications

Derivation of the viscoelastic stress in Stokes flows induced by non-spherical Brownian rigid particles through homogenization

Derivation of the viscoelastic stress in Stokes flows induced by non-spherical Brownian rigid particles through homogenization

Global existence of solutions to some equations modeling phase separation of self-propelled particles

On the stabilizing effect of swimming in an active suspension

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