| 杨巧琦,朱永刚,邓雪梅,周艳平.具部分分数阶耗散的二维不可压缩磁流体方程的稳定性[J].数学年刊A辑,2026,(1):45~58 |
| 具部分分数阶耗散的二维不可压缩磁流体方程的稳定性 |
| Stability of the 2D Incompressible Magnetohydrodynamic Equations with Partial Fractional Dissipation |
| 投稿时间：2025-10-18 修订日期：2026-01-31 |
| DOI：10.16205/j.cnki.cama.2026.0004 |
| 中文关键词: MHD方程 分数阶耗散 稳定性 |
| 英文关键词:MHD equations Fractional dissipation Stability |
| 基金项目:国家自然科学基金项目(No.11871305, No.11901346);湖北省自然科学基金项目(No.2025AFB530) |
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| 中文摘要: |
| 作者研究了具有垂直分数阶耗散νΛ22αu和分数阶磁扩散ηΛ2βb的二维不可压缩磁流体动力学方程解的稳定性. 对于该系统, 文[Feng W, Wang W, Wu J. Stability for a system of the 2D incompressible MHD equations with fractional dissipation [J]. J Math Fluid Mech, 2024, 26(4):57]建立了在Sobolev空间H3(R2)上的稳定性. 通过引入新的带有分数阶导数的各向异性不等式, 将其稳定性结果推广至更低的正则性空间H2(R2). |
| 英文摘要: |
| In this paper, the authors study the stability of solutions of the two-dimensional incompressible magnetohydrodynamic equations with fractional vertical dissipation νΛ22αu and fractional magnetic diffusion ηΛ2βb. For this system, [Feng W, Wang W, Wu J. Stability for a system of the 2D incompressible MHD equations with fractional dissipation [J]. J Math Fluid Mech, 2024, 26(4):57] established the stability in the Sobolev space H3(R2). The authors extend the result to the lower regularity space H2(R2) by introducing new anisotropic inequalities involving fractional derivatives. |
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