Díaz Díaz, Jesús IldefonsoRakotoson, Jean Michel TheresienSchmidt, Paul G.2023-06-202023-06-2020071578-7303https://hdl.handle.net/20.500.14352/49944We propose a modification of the classical Boussinesq approximation for buoyancy-driven flows of viscous, incompressible fluids in situations where viscous heating cannot be neglected. This modification is motivated by unresolved issues regarding the global solvability of the original system. A very simple model problem leads to a coupled system of two parabolic equations with a source term involving the square of the gradient of one of the unknowns. Based on adequate notions of weak and strong solutions, we establish the global-in-time existence of weak solutions and the uniqueness of strong solutions.engjournal articlehttp://www.rac.es/ficheros/doc/00271.pdfhttp://www.rac.es/racsamrestricted access517.9equationsfluidEcuaciones diferenciales1202.07 Ecuaciones en Diferencias