2016/11/25 by Tujin Kim, Daomin Cao, Kim, Tujin +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #math.AP #msc:35J87 #msc:35Q30 #msc:49J40 #msc:76D03 #msc:76D05
paper · pdf · doi:10.48550/arxiv.1611.08336
32pages
arxiv created 2016/11/25 · arxiv updated 2016/11/28
In this paper we are concerned with the steady Navier-Stokes and Stokes problems with mixed boundary conditions involving Tresca slip, leak condition, one-sided leak conditions, velocity, pressure, rotation, stress and normal derivative of velocity together. Relying on the relations among strain, rotation, normal derivative of velocity and shape of boundary surface, we have variational formulations for the problems, which consist of five formulae with five unknowns. We get the variational inequalities equivalent to the formulated variational problems, which have one unknown. Then, we study the corresponding variational inequalities and relying the results for variational inequalities, we get existence, uniqueness and estimates of solutions to the Navier-Stokes and Stokes problems with the boundary conditions. Our estimates for solutions do not depend on the thresholds for slip and leaks.