Á¦Ñ§ËùSeminar 778
±êÌ⣺INCOMPRESSIBLE FLUID FLOWS WITH SLIP BOUNDARY CONDITIONS
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ÌáÒª£º In this talk, 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 propose a complete orthogonal system of base functions, which fulfill the incompressibility and the boundary conditions exactly. It leads to an efficient spectral method. In particular, we avoid the main difficulty for ensuring the incompressibility of numerical solutions. We also derive the vorticity-stream function form with exact boundary conditions, establish some results on the existence, stability and uniqueness of its solutions, and provide an efficent spectral method. Finally, we discuss other problems with divergence-free solutions.
