Some new regularity criteria of the incompressible 3D MHD equations

Honglin Zhang; Li Li; Qingning Zhang

doi:10.1007/s10473-026-0315-y

Some new regularity criteria of the incompressible 3D MHD equations

Honglin Zhang
, Li Li^*
, Qingning Zhang

^*Corresponding author for this work

Ningbo University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we investigate several regularity criteria to the 3D incompressible magnetohydrodynamic equations. These criteria are based on certain assumptions made in partial elements of the velocity gradient tensor and pressure, respectively. By making use of the Littlewood-Paley decomposition, we show that the solution (u, b) can be smoothly extended after time T if any two groups of functions (∂₁u₁, ∂₁b₁), (∂₂u₂, ∂₂b₂) and (∂₃u₃, ∂₃b₃ belong to the space L1(0,T;B˙∞,∞0).

Original language	English
Pages (from-to)	1340-1357
Number of pages	18
Journal	Acta Mathematica Scientia
Volume	46
Issue number	3
DOIs	https://doi.org/10.1007/s10473-026-0315-y
State	Published - May 2026
Externally published	Yes

Keywords

35Q60
76D03
Besov space
Littlewood-Paley decomposition
Navier-Stokes equations
magnetohydrodynamic equations
regularity criteria

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10.1007/s10473-026-0315-y

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abstract = "In this paper, we investigate several regularity criteria to the 3D incompressible magnetohydrodynamic equations. These criteria are based on certain assumptions made in partial elements of the velocity gradient tensor and pressure, respectively. By making use of the Littlewood-Paley decomposition, we show that the solution (u, b) can be smoothly extended after time T if any two groups of functions (∂1u1, ∂1b1), (∂2u2, ∂2b2) and (∂3u3, ∂3b3 belong to the space L1(0,T;B˙∞,∞0).",

keywords = "35Q60, 76D03, Besov space, Littlewood-Paley decomposition, Navier-Stokes equations, magnetohydrodynamic equations, regularity criteria",

author = "Honglin Zhang and Li Li and Qingning Zhang",

note = "Publisher Copyright: {\textcopyright} Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences 2026.",

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doi = "10.1007/s10473-026-0315-y",

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T1 - Some new regularity criteria of the incompressible 3D MHD equations

AU - Zhang, Honglin

AU - Li, Li

AU - Zhang, Qingning

N1 - Publisher Copyright: © Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences 2026.

PY - 2026/5

Y1 - 2026/5

N2 - In this paper, we investigate several regularity criteria to the 3D incompressible magnetohydrodynamic equations. These criteria are based on certain assumptions made in partial elements of the velocity gradient tensor and pressure, respectively. By making use of the Littlewood-Paley decomposition, we show that the solution (u, b) can be smoothly extended after time T if any two groups of functions (∂1u1, ∂1b1), (∂2u2, ∂2b2) and (∂3u3, ∂3b3 belong to the space L1(0,T;B˙∞,∞0).

AB - In this paper, we investigate several regularity criteria to the 3D incompressible magnetohydrodynamic equations. These criteria are based on certain assumptions made in partial elements of the velocity gradient tensor and pressure, respectively. By making use of the Littlewood-Paley decomposition, we show that the solution (u, b) can be smoothly extended after time T if any two groups of functions (∂1u1, ∂1b1), (∂2u2, ∂2b2) and (∂3u3, ∂3b3 belong to the space L1(0,T;B˙∞,∞0).

KW - 35Q60

KW - 76D03

KW - Besov space

KW - Littlewood-Paley decomposition

KW - Navier-Stokes equations

KW - magnetohydrodynamic equations

KW - regularity criteria

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DO - 10.1007/s10473-026-0315-y

M3 - 文章

AN - SCOPUS:105039323541

SN - 0252-9602

VL - 46

SP - 1340

EP - 1357

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 3

ER -

Some new regularity criteria of the incompressible 3D MHD equations

Abstract

Keywords

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