Premium
Navier–Stokes equations with slip boundary conditions
Author(s) -
Guo Benyu
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.932
Subject(s) - mathematics , uniqueness , compact space , navier–stokes equations , vorticity , mathematical analysis , boundary value problem , compressibility , stream function , slip (aerodynamics) , boundary (topology) , stability (learning theory) , vortex , mechanics , physics , machine learning , computer science , thermodynamics
Abstract In this paper, we consider incompressible viscous fluid flows with slip boundary conditions. We first prove the existence of solutions of the unsteady Navier–Stokes equations in n ‐spacial dimensions. Then, we investigate the stability, uniqueness and regularity of solutions in two and three spacial dimensions. In the compactness argument, we construct a special basis fulfilling the incompressibility exactly, which leads to an efficient and convergent spectral method. In particular, we avoid the main difficulty for ensuring the incompressibility of numerical solutions, which occurs in other numerical algorithms. We also derive the vorticity‐stream function form with exact boundary conditions, and establish some results on the existence, stability and uniqueness of its solutions. Copyright © 2007 John Wiley & Sons, Ltd.