Weak L²-solutions to a Stokes-like system of fourth order in bounded Lipschitz domains

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:

• Stokes-like system
• divergence operator

AMS Subject Classifications::

• 76M99; 35J55; 46N20