TY - JOUR
T1 - Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions
AU - Dilmi , M.
AU - Benseridi , H.
AU - Saadallah , A.
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 797
EP - 810
PY - 2014
DA - 2014/06
SN - 6
DO - http://doi.org/10.4208/aamm.2013.m350
UR - https://global-sci.org/intro/article_detail/aamm/49.html
KW - Free boundary problems, Bingham fluid, asymptotic approach, Tresca law, Reynolds
equation.
AB - <p style="text-align: justify;">In this paper we prove first the existence and uniqueness results for the weak solution, to the
stationary equations for Bingham fluid in a three dimensional bounded domain
with Fourier and Tresca boundary condition; then we study the asymptotic
analysis when one dimension of the fluid domain tends to zero. The strong
convergence of the velocity is proved, and a specific Reynolds limit equation
and the limit of Tresca free boundary conditions are obtained.</p>