论文标题
关于双线性估计和Navier-Stokes方程的关键唯一性类别
On bilinear estimates and critical uniqueness classes for Navier-Stokes equations
论文作者
论文摘要
我们关注的是双线性估计值和对临界空间中Navier-Stokes方程的轻度溶液的独特性。为此，我们构建了一般环境，在这种环境中，对轻度配方的双线性项的估计是正确的，而无需使用辅助规范，例如Kato TimeGeightizewightize termed norm。我们首先在抽象的关键空间中获得必要的条件，然后考虑进一步的结构，以获得基于Banach空间的BESOV，Morrey和Besov-Morrey空间中的一般类别。在不同的空间以及其他PDE中提供了应用程序的示例。据我们所知，在现有文献中没有双线性估计和在Besov-Weak-Herz空间框架中获得的独特属性。证明主要基于对相应的预性空间的特征和估计。
We are concerned with bilinear estimates and uniqueness of mild solutions for the Navier-Stokes equations in critical spaces. For that, we construct general settings in which estimates for the bilinear term of the mild formulation hold true without using auxiliary norms such as Kato time-weighted ones. We first obtain necessary conditions in abstract critical spaces and then consider further structures to obtain the estimates in general classes of Besov, Morrey and Besov-Morrey spaces based on Banach spaces. Examples of applications are provided in different spaces as well as for other PDEs. In particular, as far as we know, the bilinear estimate and the uniqueness property obtained in the framework of Besov-weak-Herz spaces are not available in the existing literature. The proofs are mainly based on characterizations and estimates on the corresponding predual spaces.
