WEAK SOLUTIONS TO KOLMOGOROV-FOKKER-PLANCK EQUATIONS: REGULARITY, EXISTENCE AND UNIQUENESS
Résumé
In this article, we establish embeddings \`a la Lions and transfer of regularity \`a 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.
Mots clés
Kolmogorov-Fokker-Planck equations
kinetic spaces
transfer of regularity
weak solutions
kinetic Cauchy problems
2010 Mathematics Subject Classification. Primary: 35K65 35R05 35D30 35Q84 35R09 Secondary: 35K70 35B65 Kolmogorov-Fokker-Planck equations kinetic spaces transfer of regularity weak solutions kinetic Cauchy problems
2010 Mathematics Subject Classification. Primary: 35K65
35R05
35D30
35Q84
35R09 Secondary: 35K70
35B65 Kolmogorov-Fokker-Planck equations
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