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Upper bounds on the number of determining modes, nodes, and volume elements for a 3D magenetohydrodynamic-$\alpha$ model
Cung The Anh,Nguyen Thi Minh Toai,Vu Manh Toi
Keywords:MHD-$\alpha$ model; determining modes; determining nodes; determining volume elements
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.