Abstract
We study the weak L
2-solutions of the Dirichlet problem for a Stokes-like system of fourth order in a bounded Lipschitz domain G ⊂ ℝ
n
(n ≥ 2). For this purpose we study the operator (where
) and its adjoint. Further we determine a subspace
such that div has there a continuous inverse. This induces an orthogonal decomposition of
. Then existence, uniqueness and a priori estimates of solutions to the system under consideration are easy consequences. With the help of the Dirichlet problem for Δ3 we construct a refined decomposition of
M
2(G).
Keywords:
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