Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

Foreign participants

Channel flows and steady variational inequalities of the Navier-Stokes type

Kracmar S.

Czech technical university,
Dep. of Techn. math,
Faculty of mechanical engineering (Praha 2)

We study a steady flow a viscous incompressible fluid in a channel with a non-Dirichlet boundary condition on the output. In order to control the kinetic energy of the fluid in the channel, we assume that possible backward flows on the output are in some sense bounded. Flow fields which satisfy this assumption fill up a convex closed subset of a certain fuction space. We formulate a variational inequality of the Navier-Stokes type on this convex set and we prove the existence of its weak solution. Moreover, we also study the question in which sense the weak solution satisfies the Navier-Stokes equations and the mixed boundary condition if the solution is smooth.

Note. Abstracts are published in author's edition

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