Large radial solutions of a polyharmonic equation with superlinear growth.
A parabolic system involving a quadratic gradient term related to the Boussinesq approximation.
We 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...
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