论文标题
Kolmogorov分数Sobolev空间中的湍流模型的局部良好性
Local well-posedness of Kolmogorov's two-equation model of turbulence in fractional Sobolev Spaces
论文作者
论文摘要
我们研究了Kolmogorov在$ d-$尺寸圆环上的湍流的两个方程式模型。首先，该解决方案的本地存在具有来自非均匀分数Sobolev空间（贝塞尔电位空间）的初始数据，并使用能量方法证明了$ s> \ frac {d} {2} $的$ h^s $。接下来，我们表明解决方案在本地存在定理保证的解决方案类别中是独一无二的。
We study Kolmogorov's two-equation model of turbulence on $d-$dimensional torus. First, the local existence of the solution with the initial data from non-homogeneous fractional Sobolev spaces (Bessel potential spaces) $H^s$ with $s>\frac{d}{2}$ is proven using energy methods. Next, we show that solutions are unique in the class of solutions guaranteed by the local existence theorem.
