Publicação
Kelvin-Voigt equations for incompressible and nonhomogeneous fluids with anisotropic viscosity, relaxation and damping
| Resumo: | 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. |
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| Autores principais: | Antontsev, S. N. |
| Outros Autores: | de Oliveira, H. B.; Khompysh, Kh. |
| Assunto: | Kelvin-Voigt equations Nonhomogeneous and incompressible fluids Anisotropic PDEs Power-laws Existence Large time behavior |
| Ano: | 2022 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade do Algarve |
| Idioma: | português |
| Origem: | Sapientia - Universidade do Algarve |
| Resumo: | 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. |
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