A thermohydraulics modelwith temperature dependent constrainton velocity fields

Takeshi Fukao; Nobuyuki Kenmochi

doi:10.3934/dcdss.2014.7.17

Article Contents

2014, Volume 7, Issue 1: 17-34. Doi: 10.3934/dcdss.2014.7.17

This issue Previous Article Doubly nonlinear parabolic equations involving variable exponents Next Article Existence and linear stability of solutions of the ballistic VSC model

A thermohydraulics model with temperature dependent constraint on velocity fields

Takeshi Fukao^1, and
Nobuyuki Kenmochi^2,

1.
Department of Mathematics, Kyoto University of Education, Fuji 1, Fukakusa Fushimi-ku, Kyoto 612-8522
2.
Department of Education, School of Education, Bukkyo University, 96 Kitahananobo-cho, Murasakino, Kita-ku, Kyoto, 603-8301

Received: February 2012

Revised: March 2013

Published online: July 2013

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Abstract

In this paper, the Navier-Stokes variational inequality with the temperature dependent constraint is considered in 3-dimensional space. This problem is motivated by an initial-boundary value problem for a thermohydraulics model in which the absolute value of the velocity field is constrained, depending on the unknown temperature. The abstract theory of nonlinear evolution equations governed by subdifferentials of time-dependent convex functionals is useful in showing the existence of a solution. In the mathematical treatment, the point of emphasis is to specify a class of time-dependence of convex constraints.

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Mathematics Subject Classification: Primary: 35K86, 49J40; Secondary: 47J20.

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