On the mean field limit for Brownian particles with Coulomb interaction in 3D
Publication
, Journal Article
Li, L; Liu, JG; Yu, P
Published in: Journal of Mathematical Physics
November 1, 2019
In this paper, we consider the mean field limit of Brownian particles with Coulomb repulsion in 3D space using compactness. Using a symmetrization technique, we are able to control the singularity and prove that the limit measure almost surely is a weak solution to the limiting nonlinear Fokker-Planck equation. Moreover, by proving that the energy almost surely is bounded by the initial energy, we improve the regularity of the weak solutions. By a natural assumption, we also establish the weak-strong uniqueness principle, which is closely related to the propagation of chaos.
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Published In
Journal of Mathematical Physics
DOI
ISSN
0022-2488
Publication Date
November 1, 2019
Volume
60
Issue
11
Related Subject Headings
- Mathematical Physics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences
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Li, L., Liu, J. G., & Yu, P. (2019). On the mean field limit for Brownian particles with Coulomb interaction in 3D. Journal of Mathematical Physics, 60(11). https://doi.org/10.1063/1.5114854
Li, L., J. G. Liu, and P. Yu. “On the mean field limit for Brownian particles with Coulomb interaction in 3D.” Journal of Mathematical Physics 60, no. 11 (November 1, 2019). https://doi.org/10.1063/1.5114854.
Li L, Liu JG, Yu P. On the mean field limit for Brownian particles with Coulomb interaction in 3D. Journal of Mathematical Physics. 2019 Nov 1;60(11).
Li, L., et al. “On the mean field limit for Brownian particles with Coulomb interaction in 3D.” Journal of Mathematical Physics, vol. 60, no. 11, Nov. 2019. Scopus, doi:10.1063/1.5114854.
Li L, Liu JG, Yu P. On the mean field limit for Brownian particles with Coulomb interaction in 3D. Journal of Mathematical Physics. 2019 Nov 1;60(11).
Published In
Journal of Mathematical Physics
DOI
ISSN
0022-2488
Publication Date
November 1, 2019
Volume
60
Issue
11
Related Subject Headings
- Mathematical Physics
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences