Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 27 min ago
PreprintCC BY 4.0arXiv

On the Invertibility of the Potential-Density Mapping for the Vlasov-Poisson System in Analytic Spaces

  • Simon Le Bouëdec
Open at sourcePDFDOICite

Abstract

We develop the mathematical analysis of the Time-Dependent Density Functional Theory introduced by Manfredi [J. Plasma Phys., 86.2 (2020), 825860201] in the setting of Vlasov equations with a time-dependent exterior potential. In this context, we establish the invertibility of the potential-density mapping for the Vlasov-Poisson system on 𝕋d × ℝd when the exterior potential is (real-)analytic in the space variable. We also recover a Runge-Gross type Theorem for the Vlasov-Poisson equation for smooth (real-)analytic in time exterior potential. The surjectivity of the potential-density mapping is an inverse problem for the Vlasov-Poisson equation: we find the electric field that generates a given density profile on a given time interval.

Related

  1. A criterion of density for solutions of Poisson-driven SDEs
    Laurent Denis
    Probability Theory and Related FieldsPeer-reviewedLicence not statedFull text41 citedMathematical physicsHAL
  2. 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
  3. Weighted and nonlocal Poisson equations on domains with capacity density conditions
    Takanobu Hara
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Linear and Nonlinear Phase Mixing for the Gravitational Vlasov–Poisson System Under an External Kepler Potential
    Sanchit Chaturvedi, Jonathan Luk
    Archive for Rational Mechanics and AnalysisPeer-reviewedLicence not statedFull text16 citedGeneral mathematicsOpenAlex
  5. Characteristic Mapping Method for Vlasov-Poisson with BGK-collisions
    Xi-Yuan Yin, Philipp Krah, Zetao Lin +2
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingComputational physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{bouedec2026invertibility,
  title = {{On the Invertibility of the Potential-Density Mapping for the Vlasov-Poisson System in Analytic Spaces}},
  author = {Simon Le Bouëdec},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08586},
  eprint = {2609.08586},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08586},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Invertibility of the Potential-Density Mapping for the Vlasov-Poisson System in Analytic Spaces
AU  - Simon Le Bouëdec
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08586
UR  - https://arxiv.org/abs/2609.08586
AB  - We develop the mathematical analysis of the Time-Dependent Density Functional Theory introduced by Manfredi [J. Plasma Phys., 86.2 (2020), 825860201] in the setting of Vlasov equations with a time-dependent exterior potential. In this context, we establish the invertibility of the potential-density mapping for the Vlasov-Poisson system on 𝕋^d × ℝ^d when the exterior potential is (real-)analytic in the space variable. We also recover a Runge-Gross type Theorem for the Vlasov-Poisson equation for smooth (real-)analytic in time exterior potential. The surjectivity of the potential-density mapping is an inverse problem for the Vlasov-Poisson equation: we find the electric field that generates a given density profile on a given time interval.
ER  -