Lower bounds on mixing norms for the advection diffusion equation in R-d

摘要

An algebraic lower bound on the energy decay for solutions of the advection-diffusion equation in R-d with d = 2,3 is derived using the Fourier-splitting method. Motivated by a conjecture on mixing of passive scalars in fluids, a lower bound on the L-2- norm of the inverse gradient of the solution is obtained via gradient estimates and interpolation.