Solvability for equations of motion of weak aqueous polymer solutions with objective derivative

Zvyagin, A. V.

doi:10.1016/j.na.2013.05.022

Cited by 24 publications

(14 citation statements)

References 9 publications

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“…The following hypothesis is likely: the Karman vortex asymptotics for dilute polymer solutions as κ → 0 is uniform on the whole semi-axis z ≥ 0. This hypothesis is confirmed by numerical solution of problem (23), (24) for small values of κ, which are not presented here. Function d κ (γ) decreases monotonically with growth of parameter γ…”

Section: Motion In a Half-space Induced By Plane Rotationsupporting

confidence: 71%

“…Let us note an important specific feature of problem (23), (24). The function h, which is a coefficient at the higher derivatives in the first two equations of system (23), has a zero point of the second order at z = 0.…”

Section: Motion In a Half-space Induced By Plane Rotationmentioning

confidence: 99%

“…The correctness of the boundary-value and initial-boundary-value problems for models of motion of aqueous solutions of polymers was analyzed in [20][21][22][23][24][25]. Much more attention was paid to the second-grade fluid (see [26] with a long list of references dealing with this topic).…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions

Frolovskaya

Пухначев

2018

Polymers

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Abstract:The qualitative properties of solutions of a hereditary model of motion of aqueous solutions of polymers, its modification in the limiting case of short relaxation times, and a similar second grade fluid model are studied. Unsteady shear flows are considered. In the first case, their properties are similar to those of motion of a usual viscous fluid. Other models can include weak discontinuities, which are retained in the course of fluid motion. Exact solutions are found by using the group analysis of the examined systems of equations. These solutions describe the fluid motion in a gap between coaxial rotating cylinders, the stagnation point flow, and the motion in a half-space induced by plane rotation (analog of the Karman vortex). The problem of motion of an aqueous solution of a polymer in a cylindrical tube under the action of a streamwise pressure gradient is considered. In this case, a flow with straight-line trajectories is possible (analog of the Hagen-Poiseuille flow). In contrast to the latter, however, the pressure in the flow considered here depends on all three spatial variables.

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Section: Motion In a Half-space Induced By Plane Rotationsupporting

confidence: 71%

Section: Motion In a Half-space Induced By Plane Rotationmentioning

confidence: 99%

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Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions

Frolovskaya

Пухначев

2018

Polymers

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“…The proof of this theorem [4,5] is based on the Leray-Schauder theory of topological degree for completely continuous vector fields. The first step is the proof of a priori bound for solutions to the problem under consideration.…”

Section: Proof Of Solvability Of Initial Boundary-value Problem (1) (2)mentioning

confidence: 99%

Solvability of termoviscoelasticity problem for certain Oskolkov’s model

Zvyagin

Orlov

2014

Russ Math.

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“…In the monograph [3], a detailed description is provided for the Oskolkov model as well as for some of its modifications (in particular, the weak solvability of problem (1.1), (1.2) for θ = 0 with a total derivative in a rheological relation was established). In [4], the weak solvability of a particular initial boundary-value problem for θ = 0 with a true derivative in a rheological relation was proved.…”

Section: Introductionmentioning

confidence: 99%

Solvability of the thermoviscoelasticity problem for linearly elastically retarded voigt fluid

Zvyagin

Orlov

2015

Math Notes

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Solvability for equations of motion of weak aqueous polymer solutions with objective derivative

Cited by 24 publications

References 9 publications

Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions

Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions

Solvability of termoviscoelasticity problem for certain Oskolkov’s model

Solvability of the thermoviscoelasticity problem for linearly elastically retarded voigt fluid

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