Study of the Norton-Hoff operator coupled with the evolutive heat equation |
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Authors: | J. Ferchichi,J.P. Zolé sio |
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Affiliation: | a CMA-ENSMP, France b Research Unity: ACPDE, Department of Mathematics, Science Faculty of Monastir, Tunisia c OPALE-INRIA Sophia-Antipolis and CNRS, France |
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Abstract: | We are interested in the study of quasistatic visco-plastic flows with thermal effects. The fluid motion is governed by the incompressible Norton-Hoff model coupled with the time-dependent heat equation where the dissipated mechanical power is the source term. The viscosity of the fluid is modeled by the non-linear Arrhenius law. The well-posedness of each decoupled system is given. The optimal regularities of the heat solution and of the scale factor are supplied. A non-linear operator describing the stand coupling is provided. The existence of a solution to the considered problem is established. We prove the compactness result of the set solutions. |
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Keywords: | Visco-plastic fluid Norton-Hoff model Arrhenius law Schauder operator |
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