论文标题
动力学最大$ l^2 $ - （分数）kolmogorov方程
Kinetic maximal $L^2$-regularity for the (fractional) Kolmogorov equation
论文作者
论文摘要
我们介绍了（分数）Kolmogorov方程的动力学最大$ l^2 $ regulactility的概念。特别是，我们确定了不均匀性的函数空间和初始值，这些函数是根据分数各向异性Sobolev空间来表征分数Kolmogorov方程解决方案的规律性的。结果表明，均匀（分数）kolmogorov方程的溶液在合适的功能空间中定义了半流，并研究了瞬时正则化的特性。
We introduce the notion of kinetic maximal $L^2$-regularity with temporal weights for the (fractional) Kolmogorov equation. In particular, we determine the function spaces for the inhomogeneity and the initial value which characterize the regularity of solutions to the fractional Kolmogorov equation in terms of fractional anisotropic Sobolev spaces. It is shown that solutions of the homogeneous (fractional) Kolmogorov equation define a semi-flow in a suitable function space and the property of instantaneous regularization is investigated.
