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Multidimensional fractional material derivative — arXiv:2609.20060

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.20060
License (as archived): CC0-1.0
Archived: 2026-10-10T04:26:00.076Z
SHA-256 of the archived text: 11f5afc30b5940575f4f5643a962427ea3a443c99ad9b2ab5620c50d5c18a1dd
Stable URL of this page: https://metraipolis.com/documento/dc_7f423d733dfd

How to cite

Multidimensional fractional material derivative — arXiv:2609.20060 — arXiv (en), https://arxiv.org/abs/2609.20060 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7f423d733dfd (Metraipolis archive dc_7f423d733dfd, sha256 11f5afc30b5940575f4f5643a962427ea3a443c99ad9b2ab5620c50d5c18a1dd)

BibTeX

@misc{dc7f423d733dfd,
  title = {Multidimensional fractional material derivative — arXiv:2609.20060},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.20060},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7f423d733dfd; sha256 11f5afc30b5940575f4f5643a962427ea3a443c99ad9b2ab5620c50d5c18a1dd},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.20060. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We analyze a nonlocal operator in space and time, called the multidimensional fractional material derivative. We derive its pointwise representation, which allows us to study its other properties. We define an inverse operator, called fractional material integral, and derive its pointwise representation. Furthermore, we analyze a class of linear partial differential equations, which corresponds to deterministic descriptions of the scaling limits of multidimensional Lévy walks, in which transport is driven by a multidimensional fractional material derivative with a speed vector integrated with respect to a suitable probability measure and a distributional source term. Using Fourier-Laplace transform techniques and a direct convolution-kernel construction, we prove the existence and uniqueness of exponentially bounded measure solutions for measure data. Moreover, we identify a necessary and sufficient condition on the source term for conservation of unit mass and provide separate sufficient conditions for non-negativity and weak convergence to $\delta_0$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-18 in math.PR).
Categorie arXiv: Analysis of PDEs (math.AP) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.20060 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T04:09:58.364Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).