PreprintCC BY 4.0arXiv
Liouville Theorems for the Stationary Fractional Hall-Magnetohydrodynamic Equations
Abstract
In this paper we prove Liouville-type theorems for the stationary fractional Hall-magnetohydrodynamic equations in ℝ3. Smooth solutions vanishing at infinity, with u∈Ḣα/2 and b∈Ḣβ/2, are trivial for 1≤α≤5/3, 1≤β<2 and α+2β≤5, with no additional integrability assumption. The key step is to estimate the Hall boundary term through the Caffarelli--Silvestre extension of b.
Related
- Liouville Theorems for the Stationary Fractional Magnetohydrodynamic Equations
- Liouville-type theorems and perturbation uniqueness for stationary incompressible MHD with directional fractional dissipation
- Liouville theorems for the stationary Navier-Stokes equations under partial component conditions
- Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component
- Two improved Liouville-type theorems for the 3D stationary tropical climate model without temperature assumptions
BibTeX
@misc{ai2026liouville,
title = {{Liouville Theorems for the Stationary Fractional Hall-Magnetohydrodynamic Equations}},
author = {Albert Ai and Gaston Vergara-Hermosilla},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35260},
eprint = {2610.35260},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35260},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Liouville Theorems for the Stationary Fractional Hall-Magnetohydrodynamic Equations
AU - Albert Ai
AU - Gaston Vergara-Hermosilla
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35260
UR - https://arxiv.org/abs/2610.35260
AB - In this paper we prove Liouville-type theorems for the stationary fractional Hall-magnetohydrodynamic equations in ℝ^3. Smooth solutions vanishing at infinity, with u∈Ḣ^α/2 and b∈Ḣ^β/2, are trivial for 1≤α≤5/3, 1≤β<2 and α+2β≤5, with no additional integrability assumption. The key step is to estimate the Hall boundary term through the Caffarelli--Silvestre extension of b.
ER -