TY - JOUR
T1 - Local Existence of Strong Solutions to the Generalized MHD Equations
AU - Jin , Liangbing
AU - Cheng , Xinru
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 184
EP - 193
PY - 2024
DA - 2024/03
SN - 6
DO - http://doi.org/10.12150/jnma.2024.184
UR - https://global-sci.org/intro/article_detail/jnma/22974.html
KW - Generalized MHD system, local existence, Fourier truncation.
AB - <p style="text-align: justify;">This paper devotes to consider the local existence of the strong
solutions to the generalized MHD system with fractional dissipative terms $Λ^{2α}u$ for the velocity field and $Λ^{2α}b$ for the magnetic field, respectively. We
construct the approximate solutions by the Fourier truncation method, and use
energy method to obtain the local existence of strong solutions in $H^s
(\mathbb{R}^n)$ $(s &gt;
max \{\frac{n}{2} + 1 − 2α, 0\})$ for any $α ≥ 0.$</p>