Patrick Phelps, Temple University
Abstract: The 2D incompressible inviscid Boussinesq equations model fluid with density variations due to temperature difference. Their similarity to the 3D axisymmetric Euler equations make them a good model for studying the blow up of the 3D Euler equations. Recently, Ignatova published work on the Voigt Regularized 2D Boussinesq equations, and fractional Boussinesq equations which generate statistical solutions to the Boussinesq equations as the regulation parameter tends to zero. We are interested in extending this work to self-similar solutions, and so we rebalance the equations with a time-dependent Voigt regularization. We present results concerning existence, uniqueness, and the structure of self-similar solutions to the 2D Time-dependent Voigt Regularized Bousssinesq equations.