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Issue ESAIM: Proc.
Volume 2, 1997
Elasticity, viscoelasticity and optimal control
Page(s) 55 - 63
DOI http://dx.doi.org/10.1051/proc:1997014

ESAIM: Proc., 1997, Vol. 2, pp. 55-63
DOI: 10.1051/proc:1997014

Nonstationary flows with viscous heating effects

Thierry Clopeau and Andro Mikelic

Laboratoire d'Analyse Numérique, Bât. 101, Université Lyon 1, 43 bd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France


Abstract
The system of equations describing a nonstationary flow of a quasi-newtonian fluid, with temperature dependent viscosity and with the viscous heating, is considered. Existence of at least one weak solution is proved, i.e. we get existence of at least one velocity field having finite energy and existence of a nonnegative temperature field. Its regularity is a consequence of the nonnegative forcing term generated by the viscous heating and being only integrable.



© EDP Sciences, ESAIM 1997


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