Article ID Journal Published Year Pages File Type
4609311 Journal of Differential Equations 2016 19 Pages PDF
Abstract

This paper studies the regularity problem for the 3D incompressible resistive viscous Hall-magneto-hydrodynamic (Hall-MHD) system. The Kolmogorov 41 phenomenological theory of turbulence [14] predicts that there exists a critical wavenumber above which the high frequency part is dominated by the dissipation term in the fluid equation. Inspired by this idea, we apply an approach of splitting the wavenumber combined with an estimate of the energy flux to obtain a new regularity criterion. The regularity condition presented here is weaker than conditions in the existing criteria (Prodi–Serrin type criteria) for the 3D Hall-MHD system.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
,