Bärwolff, GünterHinze, Michael2022-05-112022-05-112008-02-222197-8085https://depositonce.tu-berlin.de/handle/11303/16894http://dx.doi.org/10.14279/depositonce-15672This preprint is a revised version of Preprint 38-2007.In the present paper we complement a recent applied work with presenting the analytical framework for general optimal boundary control problems of the Boussinesq approximation. We prove existence of optimal controls, use results of Gajewski (1975) to prove existence and uniqueness of solutions to state and the adjoint system, and derive first order necessary as well as second order sufficient optimality conditions.en510 Mathematiktime-dependent Boussinesq approximationoptimal boundary controloptimality conditionsResearch Paper