论文标题
具有关键散失的Leray方程的全球规律性和衰减行为及其应用于自相似的解决方案
Global regularity and decay behavior for Leray equations with critical-dissipation and Its Application to Self-similar Solutions
论文作者
论文摘要
在本文中，我们显示了全球规律性和薄弱解决方案的最佳衰减，这些解决方案对普遍的LERAY问题进行了严重耗散。我们的方法基于最大平滑效果，$ l^{p} $ - 类型的线性化椭圆规则，以及Laplace操作员分数产生的热半群的作用，对Annulus中支持的傅立叶变换的分布。作为副产品，我们将建立一个自相似的解决方案，以实现三维不可压缩的Navier-Stokes方程，更重要的是，证明了全球规律性和最佳衰减，而无需其他现有文献的要求。
In this paper, we show the global regularity and the optimal decay of weak solutions to the generalized Leray problem with critical dissipation. Our method is based on the maximal smoothing effect, $L^{p}$-type elliptic regularity of linearization, and the action of the heat semigroup generated by the fractional powers of Laplace operator on distributions with Fourier transforms supported in an annulus. As a by-product, we shall construct a self-similar solution to the three-dimensional incompressible Navier-Stokes equations, and more importantly, prove the global regularity and the optimal decay without additional requirement of existing literatures.
