Mathematical Dynamic Flow Models, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 10 July 2025 | Viewed by 427

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Departamento de Matemática e CIMA, Universidade de Évora, Évora, Portugal
Interests: mathematical analysis and numerical methods for ODE and PDE; with applications related with fluid mechanics
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Institute of Earth Sciences, University of Evora, 7000-645 Évora, Portugal
Interests: earthquake source seismology and seismic risk; 3D structure velocity models; strong ground motion modelling; seismotectonics and geodynamic; instrumental seismology and seismic networks; applied geophysics; geodynamic and geophysical models
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Faculty of Mechanical Engineering (FS), Czech Technical University, 166 36 Prague, Czech Republic
Interests: mathematics engineering physics and astronomy computer science medicine; fluids
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Special Issue Information

Dear Colleagues,

This Special Issue of MDPI journal Mathematics aims to attract both theoretical and applied research papers focusing on a wide range of topics in the areas of theoretical and applied mathematical fluid mechanics. This Special Issue is devoted to original research and review papers of high scientific value in all areas of mathematical fluid mechanics and its applications, paying special attention to mathematical models and numerical simulations relevant in various physical, geophysical, chemical, biological, and engineering applications. This Special Issue intends to collect a number of relevant articles in this branch of science, where novelties often appear not only in the theoretical field, but also in the field of applications.

Dr. Fernando Carapau
Prof. Dr. Mourad Bezzeghoud
Prof. Dr. Tomáš Bodnár
Guest Editors

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Keywords

  • mathematical models
  • newtonian fluids and non-newtonian fluids
  • unsteady and steady flows
  • dynamic flow applications
  • geodynamic models
  • numerical simulations

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Published Papers (1 paper)

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Research

18 pages, 382 KiB  
Article
The Kelvin–Voigt–Brinkman–Forchheimer Equations with Non-Homogeneous Boundary Conditions
by Evgenii S. Baranovskii, Mikhail A. Artemov, Sergey V. Ershkov and Alexander V. Yudin
Mathematics 2025, 13(6), 967; https://doi.org/10.3390/math13060967 - 14 Mar 2025
Viewed by 298
Abstract
We investigate the well-posedness of an initial boundary value problem for the Kelvin–Voigt–Brinkman–Forchheimer equations with memory and variable viscosity under a non-homogeneous Dirichlet boundary condition. A theorem about the global-in-time existence and uniqueness of a strong solution of this problem is proved under [...] Read more.
We investigate the well-posedness of an initial boundary value problem for the Kelvin–Voigt–Brinkman–Forchheimer equations with memory and variable viscosity under a non-homogeneous Dirichlet boundary condition. A theorem about the global-in-time existence and uniqueness of a strong solution of this problem is proved under some smallness requirements on the size of the model data. For obtaining this result, we used a new technique, which is based on the operator treatment of the initial boundary value problem with the consequent application of an abstract theorem about the local unique solvability of an operator equation containing an isomorphism between Banach spaces with two kind perturbations: bounded linear and differentiable nonlinear having a zero Fréchet derivative at a zero element. Our work extends the existing frameworks of mathematical analysis and understanding of the dynamics of non-Newtonian fluids in porous media. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models, 2nd Edition)
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