Kelvin-Voigt equations for incompressible and nonhomogeneous fluids with anisotropic viscosity, relaxation and damping
Antontsev S.N. de Oliveira H.B. Khompysh K.
September 2022Birkhauser
Nonlinear Differential Equations and Applications
2022#29Issue 5
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.
Anisotropic PDEs , Existence , Kelvin-Voigt equations , Large time behavior , Nonhomogeneous and incompressible fluids , Power-laws
Text of the article Перейти на текст статьи
CMAFCIO - Universidade de Lisboa, Lisbon, Portugal
Lavrentyev Institute of Hydrodynamics, SB RAS, Novosibirsk, Russian Federation
FCT - Universidade do Algarve, Faro, Portugal
Al-Farabi Kazakh National University, Almaty, Kazakhstan
CFM - Universidade Federal de Santa Catarina, Florianopolis, Brazil
CMAFCIO - Universidade de Lisboa
Lavrentyev Institute of Hydrodynamics
FCT - Universidade do Algarve
Al-Farabi Kazakh National University
CFM - Universidade Federal de Santa Catarina
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026