Analysis of a General Family of Regularized Navier-Stokes and MHD Models

ABSTRACT. We consider a general family of regularized Navier-Stokes and Magnetohydrodynamics (MHD) models on n-dimensional smooth compact Riemannian manifolds with or without boundary, with n 2. This family captures most of the specific regularized models that have been proposed and analyzed in the literature, including the Navier-Stokes equations, the Navier-Stokes-α model, the Leray-α model, the Modified Leray-α model, the Simplified Bardina model, the Navier-Stokes-Voight model, the Navier-Stokes-α-like models, and certain MHD models, in addition to representing a larger 3-parameter family of models not previously analyzed. This family of models has become particularly important in the development of mathematical and computational models of turbulence. We give a unified analysis of the entire three-parameter f models using only abstract mapping properties of the principal dissipation and smoothing operators, and then use assumptions about the specific form of the parameteri...

• Type: Journal
• Year: 2010
• Where: JNS
• Authors: Michael Holst, Evelyn Lunasin, Gantumur Tsogtgerel
• Keywords: Certain Mhd Models, JNS 2010, Model, This Family