PreprintCC BY-NC-SA 4.0arXiv
Existence and Blow-Up for Nonlinear Fokker-Planck with Controlled Drift Divergence
Abstract
We extend the global existence results for critical parameters of [Bianchini and Leccese, J. Math. Anal. Appl. (2024)] to the multidimensional problem ∂t u + div (b(t,x) u1+k) = Δu for b:ℝ×ℝd→ℝd non-autonomous fields, in the case (div b)-∈ L∞loc ([0,∞);Lp,∞(ℝd)), p>d. The proof of global existence follows the parabolic symmetrization approach of [Bandle, J. Analyse Math. (1976)] and is based on the study of the function m(t,s)=∫0s u*(t,r) dr.
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BibTeX
@misc{leccese2026existence,
title = {{Existence and Blow-Up for Nonlinear Fokker-Planck with Controlled Drift Divergence}},
author = {Giacomo Maria Leccese},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02294},
eprint = {2609.02294},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02294},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Existence and Blow-Up for Nonlinear Fokker-Planck with Controlled Drift Divergence
AU - Giacomo Maria Leccese
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02294
UR - https://arxiv.org/abs/2609.02294
AB - We extend the global existence results for critical parameters of [Bianchini and Leccese, J. Math. Anal. Appl. (2024)] to the multidimensional problem ∂_t u + div (b(t,x) u^1+k) = Δu for b:ℝ×ℝ^d→ℝ^d non-autonomous fields, in the case (div b)_-∈ L^∞_loc ([0,∞);L^p,∞(ℝ^d)), p>d. The proof of global existence follows the parabolic symmetrization approach of [Bandle, J. Analyse Math. (1976)] and is based on the study of the function m(t,s)=∫_0^s u^*(t,r) dr.
ER -