Pointwise estimates for Green's kernel of a mixed boundary value problem to the Stokes system in a polyhedral cone

2004/12/20 by Vladimir G. Maz'ya, Maz'ya, Vladimir G., Juergen Rossmann +1
Mathematics · Physics and Astronomy · #35J25 #35J55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35J25 #msc:35J55

paper · pdf · doi:10.48550/arxiv.math-ph/0412068

44 pages

arxiv created 2004/12/20 · arxiv updated 2009/12/01

Abstract

The paper deals with a mixed boundary value problem for the Stokes system in a polyhedral cone. Here different boundary conditions (in particular, Dirichlet, Neumann, free surface conditions) are prescribed on the sides of the polyhedron. The authors obtain regularity results for weak solutions in weighted L₂ Sobolev spaces and prove point estimates of Green's matrix.

Related

• Lp estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains
• Mixed boundary value problems for the Navier-Stokes system in polyhedral domains
• Green functions of mixed boundary value problems for stationary Stokes systems in two dimensions
• The Dirichlet problem for the nonstationary Stokes system in a polygon
• Global and local pointwise error estimates for finite element\n approximations to the Stokes problem on convex polyhedra