Boundary value problems for the Stokes equations with jumps in open sets
Dagmar Medková, Werner Varnhorn · Applicable Analysis · 2008
A boundary value problem for the Stokes system is studied in a cracked domain in ℝ n , n > 2, where the Dirichlet condition is specified on the boundary of the domain. The jump of the velocity and the jump of the stress tensor in the normal direction are prescribed on the crack. We construct a solution of this problem in the form of appropriate potentials and determine unknown source densities via integral equation systems on the boundary of the domain. The solution is given explicitly in the form of a series. As a consequence, a maximum modulus estimate for the Stokes system is proved.