UPPER BOUNDS ON THE NUMBER OF DETERMINING MODES, NODES, AND VOLUME ELEMENTS FOR A 3D MAGENETOHYDRODYNAMIC-<i>α</i> MODEL

Cung The Anh; Nguyen Thi Minh Toai; Vu Manh Toi

doi:10.11948/20190043

2020 Volume 10 Issue 2

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Cung The Anh, Nguyen Thi Minh Toai, Vu Manh Toi. UPPER BOUNDS ON THE NUMBER OF DETERMINING MODES, NODES, AND VOLUME ELEMENTS FOR A 3D MAGENETOHYDRODYNAMIC-α MODEL[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 624-648. doi: 10.11948/20190043

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Cung The Anh, Nguyen Thi Minh Toai, Vu Manh Toi. UPPER BOUNDS ON THE NUMBER OF DETERMINING MODES, NODES, AND VOLUME ELEMENTS FOR A 3D MAGENETOHYDRODYNAMIC-α MODEL[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 624-648. doi: 10.11948/20190043

UPPER BOUNDS ON THE NUMBER OF DETERMINING MODES, NODES, AND VOLUME ELEMENTS FOR A 3D MAGENETOHYDRODYNAMIC-α MODEL

1.
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
2.
Faculty of Computer Science and Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam

Abstract

Abstract

In this paper we give upper bounds on the number of determining Fourier modes, determining nodes, and determining volume elements for a 3D MHD-$ \alpha $ model. Here the bounds are estimated explicitly in terms of flow parameters, such as viscosity, magnetic diffusivity, smoothing length, forcing and domain size.
- MHD-α model /
- determining modes /
- determining nodes /
- determining volume elements
MSC: 76W05, 35Q35, 35B40

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References

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