Decay in time of incompressible flows (Q1402387)

The authors examine the Cauchy problem for incompressible Navier-Stokes or MHD equations with initial data given on all space. They give a proof for the time decay of the spatial \(L_2\)-norm of the solution, under the assumption that the solution of the heat equation with the same initial data decays. The proof is based on a decay estimate for the first derivatives of the solution, Duhamel's principle, and Gronwall-type arguments.