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Kinetic maximal \(L^2\)-regularity for the (fractional) Kolmogorov equation

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Abstract

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.

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Authors and Affiliations

  1. Institut für Angewandte Analysis, Universität Ulm, Helmholtzstraße 18, 89081, Ulm, Germany

    Lukas Niebel & Rico Zacher

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  1. Lukas Niebel
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  2. Rico Zacher
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Correspondence to Rico Zacher.

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Dedicated to Matthias Hieber on the occasion of his 60th birthday

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The first author is supported by a graduate scholarship (“Landesgraduiertenstipendium”) granted by the State of Baden-Wuerttemberg, Germany (Grant Number 1902 LGFG-E).

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Niebel, L., Zacher, R. Kinetic maximal \(L^2\)-regularity for the (fractional) Kolmogorov equation. J. Evol. Equ. 21, 3585–3612 (2021). https://doi.org/10.1007/s00028-021-00669-3

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