On coupled Navier–Stokes and energy equations in exterior-like domains

We investigate a class of nonlinear evolution systems modeling time-dependent flows of incompressible, viscous and heat-conducting fluids with temperature dependent transport coefficients in three-dimensional exterior-like domains. We prove a local existence theorem for the fully coupled parabolic system with a source term involving the square of the velocity gradient and a combination of Dirichlet and artificial boundary conditions.