PreprintCC BY-NC-SA 4.0arXiv
Existence and Blow-Up for Non-linear Fokker-Planck with Controlled Drift
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:(0,∞)×ℝd→ℝd non-autonomous fields, in the case b∈ L∞loc ((0,∞),Lp,∞(ℝd)), p>d≥ 2. For the critical case, we study the difference between two ordered solutions whose conserved small mass absorbs the drift. Finitely many increments then reach an arbitrary solution.
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BibTeX
@misc{leccese2026existence,
title = {{Existence and Blow-Up for Non-linear Fokker-Planck with Controlled Drift}},
author = {Giacomo Maria Leccese},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25764},
eprint = {2609.25764},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25764},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Existence and Blow-Up for Non-linear Fokker-Planck with Controlled Drift
AU - Giacomo Maria Leccese
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25764
UR - https://arxiv.org/abs/2609.25764
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:(0,∞)×ℝ^d→ℝ^d non-autonomous fields, in the case b∈ L^∞_loc ((0,∞),L^p,∞(ℝ^d)), p>d≥ 2. For the critical case, we study the difference between two ordered solutions whose conserved small mass absorbs the drift. Finitely many increments then reach an arbitrary solution.
ER -