INTEGRAL EQUATIONS METHOD AND THE TRANSMISSION PROBLEM FOR THE STOKES SYSTEM

The transmission problem for the Stokes system is studied: Delta v(+/-) = Delta p(+/-), del.v(+/-) = 0 in G(+/-), v(+) -v(-) = g, a(+)T (v(+); p(+)) n - a(-) T (v(-); p) n = f on partial derivative G(+). Here G(+) subset of R-3 is a bounded open set with Lipschitz boundary and G is the corresponding complementary open set. Using the integral equation method we study the problem in homogeneous Sobolev spaces. Under assumption that partial derivative G(+) is of class C-1 we study this problem also in Besov spaces and L-q-solutions of the problem. We show the unique solvability of the problem. Moreover, we solve the corresponding boundary integral equations by the successive approximation method.