An application of weighted Hardy spaces to the Navier-Stokes equations

摘要

In this article, we consider the mapping properties of convolution operators with smooth functions on weighted Hardy spaces H~p(w) with w belonging to Muckenhoupt class A_∞. As a corollary, one obtains decay estimates of heat semigroup on weighted Hardy spaces. After a weighted version of the div-curl lemma is established, these estimates on weighted Hardy spaces are applied to the investigation of the decay property of global mild solutions to Navier-Stokes equations with the initial data belonging to weighted Hardy spaces.