Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations
Riesz transforms on generalized Hardy spaces and a uniqueness theorem for the Navier-Stokes equations
复制标题
DOI：
10.14492/hokmj/1300108399
复制
发表时间：
2011-02
影响因子：
0.5
通讯作者：
E. Nakai;Tsuyoshi Yoneda
中科院分区：
文献类型：
--
作者：
E. Nakai;Tsuyoshi Yoneda
本文件有两个目的。设Rj（j = 1，2，. . .，n）是R上的Riesz变换。首先证明了RiRj的截断算子在广义哈代空间中的收敛性。我们的第一个结果是L（R）（1 < p < ∞）中收敛性的推广。其次，作为第一个结果的应用，我们证明了Navier-Stokes方程的一个唯一性定理。J. Kato（2003）建立了Navier-Stokes方程的解在整个空间中的唯一性，当速度场是有界的，压力场是一个BMO值的局部可积函数时，有界的初始数据。我们将其结果中的“BMO-值”部分推广到“广义Campanato空间值”。广义Campanato空间包括L1，BMO和α（0 < α < 1）阶齐次Lipschitz空间.
The purpose of this paper is twofold. Let Rj (j = 1, 2, . . . , n) be Riesz transforms on R. First we prove the convergence of truncated operators of RiRj in generalized Hardy spaces. Our first result is an extension of the convergence in L(R) (1 < p < ∞). Secondly, as an application of the first result, we show a uniqueness theorem for the Navier-Stokes equation. J. Kato (2003) established the uniqueness of solutions of the Navier-Stokes equations in the whole space when the velocity field is bounded and the pressure field is a BMO-valued locally integrable-in-time function for bounded initial data. We extend the part “BMO-valued” in his result to “generalized Campanato space valued”. The generalized Campanato spaces include L1, BMO and homogeneous Lipschitz spaces of order α (0 < α < 1).