Percorrer por autor "Khompysh, Kh."
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- Kelvin-Voigt equations for incompressible and nonhomogeneous fluids with anisotropic viscosity, relaxation and dampingPublication . Antontsev, S. N.; de Oliveira, H. B.; Khompysh, Kh.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.
- Kelvin-Voigt equations perturbed by anisotropic relaxation, diffusion and dampingPublication . Antontsev, S. N.; de Oliveira, H.B.; Khompysh, Kh.The purpose of this work is the analysis of the existence and uniqueness of weak solutions to a Kelvin-Voigt problem wherein the viscous and relaxation parts of the stress tensor are given by distinct power-laws. We assume that the viscous and relaxation terms may be fully anisotropic and that the momentum equation is perturbed by a damping term which may also be fully anisotropic. 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. The uniqueness of weak solutions is established in this case as well. For the full anisotropic problem, we show how all the anisotropic exponents of nonlinearity and all anisotropic coefficients must interact in order to be established global and local in time a priori estimates. (C) 2019 Elsevier Inc. All rights reserved.
- Strong solutions for the Navier–Stokes–Voigt equations with non-negative densityPublication . Borges de Oliveira, Hermenegildo; Khompysh, Kh.; Shakir, A. G.The aim of this work is to study the Navier–Stokes–Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated nonlinear initial-and boundary-value problem, we prove the global-in-time existence of strong solutions (velocity, density and pressure). We also establish some other regularity properties of these solutions and find the conditions that guarantee the uniqueness of velocity and density. The main novelty of this work is the hypothesis that, in some subdomain of space, there may be a vacuum at the initial moment, that is, the possibility of the initial density vanishing in some part of the space domain.