Year: 2026
Type: preprint
Abstract: We establish Liouville-type theorems for the three-dimensional stationary fractional magnetohydrodynamic (MHD) system with different orders of dissipation. Our first result shows that every smooth solution satisfying the natural homogeneous Sobolev energy conditions is trivial whenever $1\leqα\leq 5/3$ and $3\leqα+2β\leq5$, without any additional integrability assumptions on the velocity or magnetic fields. This extends previous results to new parameter regimes, including cases with $β<1$. Beyond this region, we prove a complementary Liouville theorem under suitable integrability conditions only on the radial components of the velocity and magnetic fields. The proofs rely on the Caffarelli--Silvestre extension and localized energy estimates.
Source: arXiv (Cornell University)
Authors: Ai, Albert, Vergara-Hermosilla, Gaston
Institutions: Peking University, Harbin Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223111993