A generic existence theorem for convective motions in a viscous fluid (Q1086088)

The bidimensional case of the problem of convective motions in an incompressible viscous fluid (Boussinesq approximation) is considered. Defining for any domain \(\Omega\) of \(C^ 5\), the ''\(\epsilon\)- neighbourhood of class \(C^ 5\) of \(\Omega\) '' by the set of domains \(\Omega_{\psi}=(I+\psi)\Omega\) with \(\| \psi \|_{C^ 5}<\epsilon\) the author proves that for almost every domain \(\Omega\), all the eigenvalues of the linearized operator are simple.