Logarithmically slow expansion of hot bubbles in gases

We predict a logarithmically slow expansion of hot bubbles in gases in the process of cooling. A model problem is first solved, when the temperature has compact support. Then the temperature profile decaying exponentially at large distances is considered. The periphery of the bubble is shown to remain essentially static (“glassy”) in the process of cooling until it is taken over by a logarithmically slowly expanding “core.” An analytical solution to the problem is obtained by matched asymptotic expansion. This problem gives an example of how logarithmic corrections enter dynamic scaling.