Quantitative finite-time approximation of scattering fields for Alfvén waves in ideal MHD
Abstract
In this paper, we establish a quantitative finite-time approximation of scattering fields for nonlinear Alfvén waves in three-dimensional ideal incompressible magnetohydrodynamics near a strong constant magnetic background. Using the global weighted estimates, we prove that truncating the scattering profiles at time T introduces an error in both the L∞ norm and the HN*+1 norm of order O(ε2(R+T)−δ), where ε∈ (0,1) measures the size of the initial perturbation, R≥100 is the scale parameter in the weighted energy, δ∈(0,2/3) is the exponent related to weights, and N*+1 is the Sobolev regularity order assumed for the initial data. The pointwise estimate follows from the decay of the nonlocal pressure along nonlinear characteristics, while the Sobolev estimate combines higher-order weighted pressure bounds with estimates for derivatives of the characteristic flows. Numerical experiments measure pointwise and Sobolev pressure-integral tails to verify the quadratic dependence of the initial perturbation amplitude.
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BibTeX
@misc{duan2026quantitative,
title = {{Quantitative finite-time approximation of scattering fields for Alfvén waves in ideal MHD}},
author = {Junming Duan and Mengni Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11595},
eprint = {2610.11595},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11595},
}
RIS
TY - UNPB
TI - Quantitative finite-time approximation of scattering fields for Alfvén waves in ideal MHD
AU - Junming Duan
AU - Mengni Li
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11595
UR - https://arxiv.org/abs/2610.11595
AB - In this paper, we establish a quantitative finite-time approximation of scattering fields for nonlinear Alfvén waves in three-dimensional ideal incompressible magnetohydrodynamics near a strong constant magnetic background. Using the global weighted estimates, we prove that truncating the scattering profiles at time T introduces an error in both the L^∞ norm and the H^N_*+1 norm of order O(ε^2(R+T)^−δ), where ε∈ (0,1) measures the size of the initial perturbation, R≥100 is the scale parameter in the weighted energy, δ∈(0,2/3) is the exponent related to weights, and N_*+1 is the Sobolev regularity order assumed for the initial data. The pointwise estimate follows from the decay of the nonlocal pressure along nonlinear characteristics, while the Sobolev estimate combines higher-order weighted pressure bounds with estimates for derivatives of the characteristic flows. Numerical experiments measure pointwise and Sobolev pressure-integral tails to verify the quadratic dependence of the initial perturbation amplitude.
ER -