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.