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Global solutions to the compressible Euler equations with heat transport byconvection in the whole space are shown to exist through perturbations ofDyson's isothermal affine solutions. This setting presents new difficultiesbecause of the vacuum at infinity behavior of the density. In particular, theperturbation of isothermal motion introduces a Gaussian function into ourstability analysis and a novel finite propagation result is proven to handlepotentially unbounded terms arising from the presence of the Gaussian. Crucialstabilization-in-time effects of the background motion are mitigated throughthe use of this finite propagation result however and a careful use of the heattransport formulation in conjunction with new time weight manipulations areused to establish global existence. The heat transport by convection offersunique physical insights into the model and mathematically, we use a controlledspatial perturbation in the analysis of this feature of our system which leadsus to exploit source term estimates as part of our techniques.

Global solutions to the compressible Euler equations with heat transport by convection around Dyson's isothermal affine solutions