Existence and large time behavior for generalized Kelvin-Voigt equations governing nonhomogeneous and incompressible fluids

Antontsev, S N; de Oliveira, H. B.; Khompysh, Kh

http://hdl.handle.net/10400.1/14738

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Authors

Antontsev, S N

de Oliveira, H. B.

Khompysh, Kh

Abstract(s)

Generalized Kelvin-Voigt equations governing nonhomogeneous and incompressible fluids are considered in this work. We assume that, in the momentum equation, the diffusion and relaxation terms are described by two distinct power-laws. Moreover, we assume that the momentum equation is perturbed by an extra 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. For the associated initial-boundary value problem, we study the existence of weak solutions as well as the large time behavior of the solutions.