Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 41 min ago
PreprintarXiv licencearXiv

Gradient Growth for Vlasov-Poisson in background charge distributed by Desingularized Dirac Delta

  • Sangwook Tae
Open at sourcePDFDOICite

Abstract

We prove the superlinear gradient growth for the one dimensional Vlasov-Poisson equation on the torus. We show them by first constructing the stationary solution which has a hyperbolic flow (locally). Then we perturb the solution and use the L∞ stability of the characteristic velocity field to show the superlinear growth. This proof was inspired by the work of Denisov.

Related

  1. On asymptotic expansions of the density of states for Poisson distributed random Schrödinger operators
    Jan Fischer, David Hasler, Jannis Koberstein
    arXivPreprintCC BY-NC-SA 4.0Full textMathematical physicsarXiv
  2. Hölder Gradient Estimates for (s,p)-Poisson Equations with measurable and Hölder Data
    Davide Giovagnoli, David Jesus
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Right Bregman proximal gradient with application to Poisson inverse problems
    Thibaut Modrzyk, Elie Bretin, Voichita Maxim
    HALPreprintCC BY 4.0Full textOptimisation & controlHALarXiv
  4. Density Collapse and Gradient Catastrophe in a One-Dimensional Euler--Poisson--Cattaneo System
    Qingsong Zhao
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Communication-Efficient Differentially Private Gradient Tracking for Distributed Optimization via Local Updates
    Mihitha Maithripala, Chenyang Qiu, Zongli Lin
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{tae2026gradient,
  title = {{Gradient Growth for Vlasov-Poisson in background charge distributed by Desingularized Dirac Delta}},
  author = {Sangwook Tae},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14887},
  eprint = {2609.14887},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14887},
}
RIS
TY  - UNPB
TI  - Gradient Growth for Vlasov-Poisson in background charge distributed by Desingularized Dirac Delta
AU  - Sangwook Tae
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.14887
UR  - https://arxiv.org/abs/2609.14887
AB  - We prove the superlinear gradient growth for the one dimensional Vlasov-Poisson equation on the torus. We show them by first constructing the stationary solution which has a hyperbolic flow (locally). Then we perturb the solution and use the L^∞ stability of the characteristic velocity field to show the superlinear growth. This proof was inspired by the work of Denisov.
ER  -