On the Sobolev boundedness of vector fields on compact Riemannian manifolds

Duván Cardona; Alexandre Kirilov; André Pedroso Kowacs; Wagner A.A. de Moraes

doi:10.1007/s11868-025-00714-6

On the Sobolev boundedness of vector fields on compact Riemannian manifolds

Duván Cardona
, Alexandre Kirilov^*
, André Pedroso Kowacs
, Wagner A.A. de Moraes

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We analyze the sharpness of the Sobolev order for smooth vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of eigenvalues associated with these vector fields. As an application, we demonstrate the ill-posedness of a class of Cauchy problems involving left-invariant vector fields on compact Lie groups.

Original language	English
Article number	52
Journal	Journal of Pseudo-Differential Operators and Applications
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/s11868-025-00714-6
State	Published - Sep 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

Keywords

46E35. Secondary 35S10
Fourier analysis
Global hypoellipticity
Primary 58J40
Sobolev space
Vector field
Well-posedness

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s11868-025-00714-6

Cite this

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abstract = "We analyze the sharpness of the Sobolev order for smooth vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of eigenvalues associated with these vector fields. As an application, we demonstrate the ill-posedness of a class of Cauchy problems involving left-invariant vector fields on compact Lie groups.",

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author = "Duv{\'a}n Cardona and Alexandre Kirilov and Kowacs, \{Andr{\'e} Pedroso\} and \{de Moraes\}, \{Wagner A.A.\}",

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AU - Cardona, Duván

AU - Kirilov, Alexandre

AU - Kowacs, André Pedroso

AU - de Moraes, Wagner A.A.

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

PY - 2025/9

Y1 - 2025/9

N2 - We analyze the sharpness of the Sobolev order for smooth vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of eigenvalues associated with these vector fields. As an application, we demonstrate the ill-posedness of a class of Cauchy problems involving left-invariant vector fields on compact Lie groups.

AB - We analyze the sharpness of the Sobolev order for smooth vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of eigenvalues associated with these vector fields. As an application, we demonstrate the ill-posedness of a class of Cauchy problems involving left-invariant vector fields on compact Lie groups.

KW - 46E35. Secondary 35S10

KW - Fourier analysis

KW - Global hypoellipticity

KW - Primary 58J40

KW - Sobolev space

KW - Vector field

KW - Well-posedness

UR - https://www.scopus.com/pages/publications/105009326571

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DO - 10.1007/s11868-025-00714-6

M3 - Article

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JO - Journal of Pseudo-Differential Operators and Applications

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IS - 3

M1 - 52

ER -

On the Sobolev boundedness of vector fields on compact Riemannian manifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this