Generalized Kelvin-Voigt equations for nonhomogeneous andincompressible fluids

Antontsev, Stanislav N.; de Oliveira, H.B.; Khompysh, Khonatbek

http://hdl.handle.net/10400.1/14448

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Authors

Antontsev, Stanislav N.

de Oliveira, H.B.

Khompysh, Khonatbek

Abstract(s)

In this work, we consider the Kelvin-Voigt equations for non-homogeneous and incompressible fluid flows with the diffusion and relaxation terms 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. In the case the extra term is a sink, we prove the global existence of weak solutions and we establish the conditions for the polynomial time decay and for the exponential time decay of these solutions. If the extra term is a source, we show how the exponents of nonlinearity must interact to ensure the local existence of weak solutions.