Electronic Research Archive (Jun 2024)

Analyticity estimates for the 3D magnetohydrodynamic equations

  • Wenjuan Liu ,
  • Jialing Peng

DOI
https://doi.org/10.3934/era.2024173
Journal volume & issue
Vol. 32, no. 6
pp. 3819 – 3842

Abstract

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This paper was concerned with the Cauchy problem of the 3D magnetohydrodynamic (MHD) system. We first proved that this system was local well-posed with initial data in the Besov space $ \dot{B}^{s}_{p, q}(\mathbb{R}^{3}) $, in the critical Besov space $ \dot{B}^{-1+\frac{3}{p}}_{p, q}(\mathbb{R}^{3}) $, and in $ L^{p}(\mathbb{R}^{3}) $ with $ p\in]3, 6[ $, respectively. We also obtained a new growth rate estimates for the analyticity radius.

Keywords