WIAS Preprint No. 2504, (2018)

The Boussinesq system with mixed non-smooth boundary conditions and ``do-nothing'' boundary flow


  • Ceretani, Andrea
  • Rautenberg, Carlos N.
    ORCID: 0000-0001-9497-9296

2010 Mathematics Subject Classification

  • 34A34 34B15 76D05 80A20


  • Boussinesq system, mixed boundary conditions, do nothing boundary condition




A stationary Boussinesq system for an incompressible viscous fluid in a bounded domain with a nontrivial condition at an open boundary is studied. We consider a novel non-smooth boundary condition associated to the heat transfer on the open boundary that involves the temperature at the boundary, the velocity of the fluid, and the outside temperature. We show that this condition is compatible with two approaches at dealing with the do-nothing boundary condition for the fluid: 1) the directional do-nothing condition and 2) the do-nothing condition together with an integral bound for the backflow. Well-posedness of variational formulations is proved for each problem.

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