Kelvin-Voigt equations for incompressible and nonhomogeneous fluids with anisotropic viscosity, relaxation and damping Full article
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Nonlinear Differential Equations and Applications
ISSN: 1021-9722 |
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| Output data | Year: 2022, Volume: 29, Number: 5, Article number : 60, Pages count : DOI: 10.1007/s00030-022-00794-z | ||||||||||
| Tags | Anisotropic PDEs; Existence; Kelvin-Voigt equations; Large time behavior; Nonhomogeneous and incompressible fluids; Power-laws | ||||||||||
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования Российской Федерации | FWGG-2021-0010 |
Abstract:
In this work, we consider the nonlinear initial-boundary value problem posed by the Kelvin-Voigt equations for non-homogeneous and incompressible fluid flows with fully anisotropic diffusion, relaxation and damping. Moreover, we assume that the momentum equation is perturbed by a damping term which, depending on whether its signal is positive or negative, may account for the presence of a source or a sink within the system. In the particular case of considering this problem with a linear and isotropic relaxation term, we prove the existence of global and local weak solutions for the associated initial-boundary value problem supplemented with no-slip boundary conditions. When the damping term describes a sink, we establish the conditions for the polynomial time decay or for the exponential time decay of these solutions.
Cite:
Antontsev S.N.
, de Oliveira H.B.
, Khompysh K.
Kelvin-Voigt equations for incompressible and nonhomogeneous fluids with anisotropic viscosity, relaxation and damping
Nonlinear Differential Equations and Applications. 2022. V.29. N5. 60 . DOI: 10.1007/s00030-022-00794-z WOS Scopus РИНЦ OpenAlex
Kelvin-Voigt equations for incompressible and nonhomogeneous fluids with anisotropic viscosity, relaxation and damping
Nonlinear Differential Equations and Applications. 2022. V.29. N5. 60 . DOI: 10.1007/s00030-022-00794-z WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Feb 17, 2021 |
| Accepted: | Jun 24, 2022 |
| Published print: | Jul 11, 2022 |
Identifiers:
| Web of science: | WOS:000824900300001 |
| Scopus: | 2-s2.0-85133928223 |
| Elibrary: | 53032621 |
| OpenAlex: | W4285043782 |