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Mathematics
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Mathematical Problems in Fluid Mechanics
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Mathematical Problems in Fluid Mechanics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: 28 May 2024 | Viewed by 2548

Special Issue Editors

Dr. Dmitriy Prokudin

E-Mail Website
Guest Editor
Lavrentyev Institute of Hydrodynamics, 630090 Novosibirsk, Russia
Interests: differential equations; dynamical systems; optimal control
Dr. A. V. Zvyagin

E-Mail Website
Guest Editor
Department of Algebra and Mathematical Methods of Hydrodynamics, Voronezh State University, 394018 Voronezh, Russia
Interests: control theory; mathematical modeling; nonlinear analysis; hydrodynamics; applied mathematics; differential equations; control systems; engineering; applied and computational mathematics; topology; stability
Prof. Dr. Viktor Grigor'evich Zvyagin

E-Mail Website
Guest Editor
Laboratory of Mathematical Fluid Dynamics, Voronezh State University, 394018 Voronezh, Russia
Interests: topology; mathematical analysis; functional analysis; differential equations; pure mathematics; analysis; complex analysis; real and complex analysis; applied mathematics; fluid mechanics

Special Issue Information

Dear Colleagues,

This Special Issue will focus on recent theoretical research that is related to the mathematical problems associated with fluid mechanics. Thus, we welcome contributions that attend to the following areas of interest: existence and uniqueness theorems, stability questions, regularity criteria, optimal flow control, and novel analytical solutions to Newtonian and non-Newtonian fluid flows.

Dr. Dmitriy Prokudin
Dr. A. V. Zvyagin
Prof. Dr. Viktor Grigor'evich Zvyagin
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Newtonian and non-Newtonian fluids
  • mathematical modeling
  • boundary-value problems
  • existence and uniqueness theorems
  • stability questions
  • regularity criteria
  • optimal control problems
  • exact solutions

Published Papers (4 papers)

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Research

27 pages, 404 KiB  
Article
Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories
by Mikhail Turbin and Anastasiia Ustiuzhaninova
Mathematics 2024, 12(2), 266; https://doi.org/10.3390/math12020266 - 14 Jan 2024
Viewed by 504
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Mathematical Problems in Fluid Mechanics)
15 pages, 362 KiB  
Article
Equilibrium Figures for a Rotating Compressible Capillary Two-Layer Liquid
by Irina Vladimirovna Denisova and Vsevolod Alexeevich Solonnikov
Mathematics 2024, 12(1), 94; https://doi.org/10.3390/math12010094 - 27 Dec 2023
Viewed by 450
Abstract
The paper proves the existence of a family of axisymmetric equilibrium figures as solutions of a stationary problem with unknown boundaries for the Navier–Stokes equations corresponding to the slow rotation of a viscous compressible two-layer liquid mass about some axis. It is assumed [...] Read more.
The paper proves the existence of a family of axisymmetric equilibrium figures as solutions of a stationary problem with unknown boundaries for the Navier–Stokes equations corresponding to the slow rotation of a viscous compressible two-layer liquid mass about some axis. It is assumed that the liquids are barotropic and capillary, and have different viscosities, the internal fluid being bounded by a closed surface. This interface does not intersect with the external boundary of the cloud. The proof is based on implicit function theorem and carried out in the Hölder spaces. Full article
(This article belongs to the Special Issue Mathematical Problems in Fluid Mechanics)
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25 pages, 748 KiB  
Article
Lateral-Concentration Inhomogeneities in Flows of Suspensions of Rod-like Particles: The Approach of the Theory of Anisotropic Micropolar Fluid
by Vladimir Shelukhin
Mathematics 2023, 11(23), 4740; https://doi.org/10.3390/math11234740 - 23 Nov 2023
Viewed by 486
Abstract
To tackle suspensions of particles of any shape, the thermodynamics of a Cosserat continuum are developed by the method suggested by Landau and Khalatnikov for the mathematical description of the super-fluidity of liquid 2He. Such an approach allows us to take into account [...] Read more.
To tackle suspensions of particles of any shape, the thermodynamics of a Cosserat continuum are developed by the method suggested by Landau and Khalatnikov for the mathematical description of the super-fluidity of liquid 2He. Such an approach allows us to take into account the rotation of particles and their form. The flows of suspensions of neutrally buoyant rod-like particles are considered in detail. These suspensions include linear polymer solutions, FD-virus and worm-like micelles. The anisotropy of the suspensions is determined through the inclusion of the micro-inertia tensor in the rheological constitutive equations. The theory predicts gradient banding, temporal volatility of apparent viscosity and hysteresis of the flux-pressure curve. The transition from the isotropic phase to the nematic phase is also captured. Our mathematical model predicts the formation of flock-like inhomogeneities of concentration jointly with the hindrance effect. Full article
(This article belongs to the Special Issue Mathematical Problems in Fluid Mechanics)
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11 pages, 293 KiB  
Article
On the Stabilization of the Solution to the Initial Boundary Value Problem for One-Dimensional Isothermal Equations of Viscous Compressible Multicomponent Media Dynamics
by Dmitriy Prokudin
Mathematics 2023, 11(14), 3065; https://doi.org/10.3390/math11143065 - 11 Jul 2023
Cited by 1 | Viewed by 621
Abstract
An initial boundary value problem is considered for one-dimensional isothermal equations of the dynamics of viscous compressible multicomponent media, which are a generalization of the Navier–Stokes equations. The stabilization of the solution to the initial boundary value problem is proven while the time [...] Read more.
An initial boundary value problem is considered for one-dimensional isothermal equations of the dynamics of viscous compressible multicomponent media, which are a generalization of the Navier–Stokes equations. The stabilization of the solution to the initial boundary value problem is proven while the time tends to infinity, without simplifying assumptions for the structure of the viscosity matrix, except for the standard physical requirements of symmetry and positive definiteness. It is shown that the stabilization of the solution is exponential. Full article
(This article belongs to the Special Issue Mathematical Problems in Fluid Mechanics)
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