On the Influence of an Absorption Term in Incompressible Fluid Flows
This work is concerned with a mathematical problem derived from the Ellis model used in Fluid Mechanics to describe the response of a great variety of generalized fluid flows. For pseudoplastic fluids, it is well-known that the weak solutions to that problem extinct in a finite time. In order to obtain the same property for Newtonian and dilatant fluids, we modify the problem by introducing an absorption term in the momentum equation. The proof relies on a suitable energy method, Sobolev type interpolation inequalities and also on a generalized Korn’s inequality. Then we extend our results for several cases: slip boundary conditions, anisotropic absorption and non-homogeneous fluid flows.We also discuss existence and uniqueness of weak solutions for the modified problem.
KeywordsNon-Newtonian fluids Ellis model Absorption Existence Uniqueness Extinction in time
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