Díaz Díaz, Jesús IldefonsoRakotoson, J.M.Schmidt, P.G.2023-06-202023-06-2020081079-9389https://hdl.handle.net/20.500.14352/51369We propose a modification of the classical Navier-Stokes-Boussinesq system of equations, which governs buoyancy-driven flows of viscous, incompressible fluids. This modification is motivated by unresolved issues regarding the global solvability of the classical system in situations where viscous heating cannot be neglected. A 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. In the present paper, we establish the local-in-time existence and uniqueness of strong solutions for the model problem. The full system of equations and the global-in-time existence of weak solutions will be addressed in forthcoming work.engjournal articlehttp://projecteuclid.org/euclid.ade/1355867327http://www.aftabi.com/open access517.9Boussinesq approximationviscous heatingparabolic systemstrong solutions.Ecuaciones diferenciales1202.07 Ecuaciones en Diferencias