Georgia Institute of Technology College of Sciences

In this talk, firstly, we study the local and global well-posedness for full Navier-Stokes equations with temperature dependent coefficients in the framework of Besov space. We generalized R. Danchin's results for constant transport coefficients to obtain the local and global well-posedness for the initial with low regularity in Besov space framework. Secondly, we give a time decay rate results of the global solution in the Besov space framework which is not investigated before. Due to the low regularity assumption, we find that the high frequency part is also important for us to get the time decay.