Kinetic maximal L²-regularity for the (fractional) Kolmogorov\n equation

2020/06/20 by Lukas Niebel, Niebel, Lukas, Rico Zacher +1
Mathematics · #35B65 #35H10 #35K65 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2006.11531

openalex publication_date 2020/06/20 · openalex created_date 2025/10/26 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of kinetic maximal L²-regularity with temporal\nweights for the (fractional) Kolmogorov equation. In particular, we determine\nthe function spaces for the inhomogeneity and the initial value which\ncharacterize the regularity of solutions to the fractional Kolmogorov equation\nin terms of fractional anisotropic Sobolev spaces. It is shown that solutions\nof the homogeneous (fractional) Kolmogorov equation define a semi-flow in a\nsuitable function space and the property of instantaneous regularization is\ninvestigated.\n

Citations

• Zufallige Bewegungen (Zur Theorie der Brownschen Bewegung)

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