Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness. - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness.

Pascal Auscher
  • Function : Author
  • PersonId : 1166838
  • IdRef : 073281530
Lukas Niebel
  • Function : Author
  • PersonId : 1367348

Abstract

In this article, we establish embeddings à la Lions and transfer of regularity à la Bouchut for a large scale of kinetic spaces. We use them to identify a notion of weak solutions to Kolmogorov-Fokker-Planck equations with (local or integral) diffusion and rough (measurable) coefficients under minimal requirements. We prove their existence and uniqueness for a large class of source terms, first in full space for the time, position and velocity variables and then for the kinetic Cauchy problem on infinite and finite time intervals.
Fichier principal
Vignette du fichier
weaksol_KFP-final2.pdf (542.34 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Licence

Dates and versions

hal-04519638 , version 1 (25-03-2024)
hal-04519638 , version 2 (07-04-2024)

Licence

Identifiers

Cite

Pascal Auscher, Cyril Imbert, Lukas Niebel. Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness.. 2024. ⟨hal-04519638v2⟩
42 View
10 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More