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PreprintCC BY-NC-ND 4.0arXiv

Spontaneous Geometric Structures in 2D MHD Flows

  • Matheus Nasi
  • Cilon F. Perusato
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Abstract

Under suitable spatial decay assumptions on the initial data, we establish precise asymptotic expansions of the velocity and magnetic fields for two-dimensional incompressible MHD flows at each positive time. We identify in the far-field profile the hexagonal pattern previously discovered for the 2D Navier-Stokes equations by L. Brandolese \cite{Bra22}, characterized by six equally spaced directions of faster decay for each component of u(x,t)−u0(x). Surprisingly, the corresponding contribution to the magnetic field vanishes identically, owing to an exact cancellation associated with the antisymmetric structure of the magnetic nonlinearity. Thus, at order |x|−3, the hexagonal structure appears only in the velocity field.

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Cite

BibTeXRIS
BibTeX
@misc{nasi2026spontaneous,
  title = {{Spontaneous Geometric Structures in 2D MHD Flows}},
  author = {Matheus Nasi and Cilon F. Perusato},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01579},
  eprint = {2611.01579},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01579},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Spontaneous Geometric Structures in 2D MHD Flows
AU  - Matheus Nasi
AU  - Cilon F. Perusato
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01579
UR  - https://arxiv.org/abs/2611.01579
AB  - Under suitable spatial decay assumptions on the initial data, we establish precise asymptotic expansions of the velocity and magnetic fields for two-dimensional incompressible MHD flows at each positive time. We identify in the far-field profile the hexagonal pattern previously discovered for the 2D Navier-Stokes equations by L. Brandolese \cite{Bra22}, characterized by six equally spaced directions of faster decay for each component of u(x,t)−u_0(x). Surprisingly, the corresponding contribution to the magnetic field vanishes identically, owing to an exact cancellation associated with the antisymmetric structure of the magnetic nonlinearity. Thus, at order |x|^−3, the hexagonal structure appears only in the velocity field.
ER  -