Analysis of the Stationary Thermal-Electro Hydrodynamic Boussinesq Equations

  • Philipp Gerstner (Author)
    Engineering Mathematics and Computing Lab (EMCL), Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University
  • Martin Baumann (Author)
    Engineering Mathematics and Computing Lab (EMCL), Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University
  • Vincent Heuveline (Author)
    Engineering Mathematics and Computing Lab (EMCL), Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University

Abstract

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.

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Published
2019-04-14