Some local estimates and a uniqueness result for the entire biharmonic heat equation

We consider smooth solutions to the biharmonic heat equation on ℝn x [0,T] for which the square of the Laplacian at time t is globally bounded from above by k0/t for some k0 in ℝ+, for all t ∈ [0,T]. We prove local, in space and time, estimates for such solutions. We explain how these estimates imply uniqueness of smooth solutions in this class.