High-temperature viscous flows. A case of pudding model

We investigate the Navier-Stokes-Fourier system for incompressible heat conducting inhomogeneous fluid. The main result concerns existence of global in time regular large solutions, provided the initial temperature is sufficiently large. Magnitudes of norms of initial velocity and gradients of initial temperature and density are not limited. The system may be viewed as a model of pudding, as we assume the viscosity grows with the temperature.