Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the $$L^p$$ L p framework

Hua Qiu () and Zheng-an Yao ()
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Hua Qiu: South China Agricultural University
Zheng-an Yao: Sun Yat-sen University

Partial Differential Equations and Applications, 2022, vol. 3, issue 6, 1-38

Abstract: Abstract In this paper, we consider the Cauchy problem of the d-dimensional magnetohydrodynamic (MHD) system with the fractional dissipation $$(-\Delta )^{\alpha }u$$ ( - Δ ) α u and without the magnetic diffusion. We obtain the local existence and uniqueness of the solution to the non-resistive MHD system in the $$L^p$$ L p framework under two cases: $$\alpha \ge 1$$ α ≥ 1 and $$\alpha

Keywords: Magnetohydrodynamic system; Weak solution; Uniqueness; Besov spaces; 35A02; 35Q35; 76D03 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s42985-022-00211-1

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