热方程的一些端点估计及其在Navier-Stokes方程中的应用

Some endpoint estimates for heat equation with application to Navier-Stokes equations

本文首先讨论热方程初值问题的解在Hardy、BMO(bounded mean oscillation)和Besov型空间中的估计.然后本文结合Coifmann-Lions-Meyer-Semmes在Hardy空间中的补偿紧性结果,给出Navier-Stokes方程整体弱解的二阶导数的一些端点估计.

We obtain some estimates in Hardy, BMO and Besov spaces for solutions to the initial value problem of heat equation. Combined with Coifmann-Lions-Meyer-Semmes＇ result on compensated compactness in Hardy spaces, we also give some endpoint estimates for the second order derivatives of global weak solutions to Navier- Stokes equations.