Analysis of the sationary thermal-electro hydrodynamic Boussinesq equations - Gerstner, Philipp; Baumann, Martin; Heuveline, Vincent (Preprint series of the Engineering Mathematics and Computing Lab (EMCL), 2019)
A functional analytic framework is proposed for setting up the variational formulation of the stationary, thermal-electro hydrodynamical Boussinesq equations. In this setting, existence, stability and uniqueness of solutions in a suitable Sobolev space is shown. The results are obtained by extending the existing theory on stationary Boussinesq equations to take into account a more general force term and by employing a fixed-point argument for augmenting the Boussinesq equations with Gauss' law and the dielectrophoretic force.