Local and global solutions to Stokes-Magneto equations with fractional dissipations

Hantaek Bae (), Hyunwoo Kwon () and Jaeyong Shin ()
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Hantaek Bae: Ulsan National Institute of Science and Technology (UNIST)
Hyunwoo Kwon: Brown University
Jaeyong Shin: Yonsei University

Partial Differential Equations and Applications, 2025, vol. 6, issue 4, 1-23

Abstract: Abstract In this paper, we investigate a Stokes-Magneto system with fractional diffusions. We first deal with the non-resistive case in $${\mathbb {T}}^{d}$$ T d and establish the local and global well-posedness with initial magnetic field $${\varvec{b}}_0\in H^{s}({\mathbb {T}}^d).$$ b 0 ∈ H s ( T d ) . We also show the existence of a unique mild solution of the resistive case with initial data $${\varvec{b}}_0$$ b 0 in the critical $$L^{p}({\mathbb {R}}^d)$$ L p ( R d ) space. Moreover, we show that $$\Vert {\varvec{b}}(t)\Vert _{L^{p}}$$ ‖ b ( t ) ‖ L p converges to zero as $$t\rightarrow \infty $$ t → ∞ when the initial data is sufficiently small.

Keywords: Global existence; Uniqueness; Strong solutions; Mild solutions; Fractional diffusions; 35Q35; 76W05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00341-2

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