Attractors of equations of non-Newtonian fluid dynamics

Zvyagin, V. G.; Kondrat'ev, Stanislav Konstantinovich

doi:10.1070/rm2014v069n05abeh004918

Cited by 24 publications

(6 citation statements)

References 26 publications

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“…Let us present some facts from the theory of trajectory attractors. This presentation does not pretend to be complete and contains only those facts that we will directly need (for more details, see monograph [8], as well as articles [9,33]).…”

Section: Necessary Definitions and Statements From Attractor Theorymentioning

confidence: 99%

“…We use the already-traditional notation ∥u − v∥ C(R + ;E 0 ) for the metric in C(R + ; E 0 ). This is due to the use of abstract concepts and statements from [8,33], in which this notation is used. Note that the functional ∥…”

Section: Necessary Definitions and Statements From Attractor Theorymentioning

confidence: 99%

“…In this paper, the existence of trajectory and global attractors is established for a system of equations corresponding to the Kelvin-Voigt model with rheological relation (1) under certain conditions on the coefficients of the problem. The proof is carried out using the approximation-topological approach to the study of fluid dynamic problems (see, for example, [15]), as well as the theory of trajectory and global attractors for non-invariant trajectory spaces [8,33]. Namely, some problem that approximates the original one is considered.…”

Section: Introductionmentioning

confidence: 99%

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Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories

Turbin,

Ustiuzhaninova

2024

Mathematics

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This article is devoted to the study of the existence of trajectory and global attractors in the Kelvin–Voigt fluid model, taking into account memory along the trajectories of fluid motion. For the model under study, the concept of a weak solution on a finite segment and semi-axis is introduced and the existence of their solutions is proved. The necessary exponential estimates for the solutions are established. Then, based on these estimates, the existence of trajectory and global attractors in the problem under study is proved.

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Section: Necessary Definitions and Statements From Attractor Theorymentioning

confidence: 99%

Section: Necessary Definitions and Statements From Attractor Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories

Turbin,

Ustiuzhaninova

2024

Mathematics

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“…These papers feature the attractors of three-dimensional Navier-Stokes equations, which are notorious for its lack of uniqueness of weak solutions, and became a breakthrough in the analysis of indeterministic dynamics. The theory was further developed in [3,4,5,6,7], see also the reviews [8,9,10] and monographs [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Pullback attractors of the Jeffreys–Oldroyd equations

Zvyagin

Kondratyev

2016

Journal of Differential Equations

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We study the dynamics of the Jeffreys-Oldroyd equation using the theory of trajectory pullback attractors. We prove an existence theorem for weak solutions and use it to construct a family of trajectory spaces and to specify the class of attracted families of sets, which includes families bounded in the past. Finally, we prove the existence of the trajectory and global pullback attractors of the model.

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“…В различных задачах математической гидродинамики часто не представляется возможным установить единственность решения эволюционной задачи с заданным начальным условием. В таких случаях динамика уравнения описывается в терминах пространств траекторий [2]- [6], и наряду с притягивающими множествами в фазовом пространстве рассматриваются так называемые траекторные аттракторы. Составляющими элементами последних являются функции времени, на которые "становятся похожи" траектории системы.…”

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Pullback attractors for the model of motion of dilute aqueous polymer solutions

Звягин¹,

Zvyagin²,

Kondrat'ev³

2015

Известия Российской академии наук. Серия математическая

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Pullback-аттракторы модели движения слабо концентрированных водных растворов полимеров Изучается качественная динамика слабых решений неавтономной модели движения слабо концентрированных водных растворов полимеров на основании теории pullback-аттракторов пространств траекторий. Для рассматриваемой модели устанавливается существование слабых решений, определяется семейство пространств траекторий, вводится понятие траекторного и минимального pullback-аттракторов и доказывается существование этих аттракторов. Библиография: 15 наименований. Ключевые слова: pullback-аттракторы, пространство траекторий, слабо концентрированные водные растворы полимера, слабые решения, теоремы существования.

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Attractors of equations of non-Newtonian fluid dynamics

Cited by 24 publications

References 26 publications

Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories

Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories

Pullback attractors of the Jeffreys–Oldroyd equations

Pullback attractors for the model of motion of dilute aqueous polymer solutions

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