The classical Kelvin–Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity

DOI10.1088/1361-6544/abe51ezbMath1468.35125OpenAlexW3162093851MaRDI QIDQ4990892

Kh Khompysh, Hermenegildo Borges de Oliveira, Stanislav N. Antontsev

Publication date: 1 June 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/abe51e

zbMATH Keywords

regularityexistenceuniquenessKelvin-Voigt equationsincompressible fluids with non-constant density

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Viscoelastic fluids (76A10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (10)

Kelvin-Voigt equations for incompressible and nonhomogeneous fluids with anisotropic viscosity, relaxation and damping ⋮ Existence and regularity of strong solutions to a nonhomogeneous Kelvin-Voigt-Cahn-Hilliard system ⋮ An existence theorem for weak solutions of the initial-boundary value problem for the inhomogeneous incompressible Kelvin-Voigt model in which the initial value of density is not bounded from below ⋮ Solvability of the initial-boundary value problem for the Kelvin-Voigt fluid motion model with variable density ⋮ Inverse problems for a Boussinesq system for incompressible viscoelastic fluids ⋮ Weak solvability of the initial-boundary value problem for inhomogeneous incompressible Kelvin-Voigt fluid motion model of arbitrary finite order ⋮ On an inverse problem for a linearized system of Navier-Stokes equations with a final overdetermination condition ⋮ Existence of weak solution to initial-boundary value problem for finite order Kelvin-Voigt fluid motion model ⋮ Cauchy problem for the Navier-Stokes-Voigt model governing nonhomogeneous flows ⋮ An inverse problem for generalized Kelvin–Voigt equation with p-Laplacian and damping term

Cites Work

• Unnamed Item
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• Sobolev inequalities in arbitrary domains
• Kelvin-Voight equation with \(p\)-Laplacian and damping term: existence, uniqueness and blow-up
• On the structural stability of the Euler-Voigt and Navier-Stokes-Voigt models
• Suitable weak solutions to the 3D Navier-Stokes equations are constructed with the Voigt approximation
• Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models
• On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model
• Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit
• Global attractors and determining modes for the 3D Navier-Stokes-Voight equations
• Existence of axisymmetric solutions of the stationary system of Navier-Stokes equations in a class of domains with noncompact boundary
• Fluid dynamics of viscoelastic liquids
• Unique solvability of an initial- and boundary-value problem for viscous incompressible nonhomogeneous fluids
• The uniqueness and global solvability of boundary-value problems for the equations of motion for aqueous solutions of polymers
• Nonlocal problems for the equations of the Kelvin-Voigt fluids and their \(\varepsilon\)-approximations
• On some gaps in two of my papers on the Navier-Stokes equations and the way of closing them
• Optimal feedback control in the problem of the motion of a viscoelastic fluid
• On the Bardina's model in the whole space
• Turbulent flows as generalized Kelvin-Voigt materials: modeling and analysis
• Generalized Kelvin-Voigt equations for nonhomogeneous and incompressible fluids
• Generalized Kelvin-Voigt equations with \(p\)-Laplacian and source/absorption terms
• The study of initial-boundary value problems for mathematical models of the motion of Kelvin-Voigt fluids
• On a well-posed turbulence model
• On weak solutions of the equations of motion of a viscoelastic medium with variable boundary
• Kelvin-Voigt equations perturbed by anisotropic relaxation, diffusion and damping
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• Nonhomogeneous Viscous Incompressible Fluids: Existence of Velocity, Density, and Pressure
• Kelvin–Voigt equations with anisotropic diffusion, relaxation and damping: Blow-up and large time behavior
• Sobolev Spaces

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