Inertial Manifolds for 2D Generalized MHD System

Zhaoqin Yuan,Liang Guo,Guoguang Lin

doi:10.4236/ijmnta.2015.43014

Zhaoqin Yuan, Liang Guo + Show 1 more

Open Access

https://doi.org/10.4236/ijmnta.2015.43014

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Abstract

In this paper, we prove the existence of inertial manifolds for 2D generalized MHD system under the spectral gap condition.

Highlights

In [1], Yuan, Guo and Lin prove the existence of global attractors and dimension estimation of a 2D generalized magnetohydrodynamic (MHD) system: ∂u ∂t + (u ⋅∇) u − (v ⋅ ∇)
We prove the existence of inertial manifolds for 2D generalized MHD system under the spectral gap condition
More results about inertial manifolds can be founded in [2]-[11]

Summary

Introduction

In [1], Yuan, Guo and Lin prove the existence of global attractors and dimension estimation of a 2D generalized magnetohydrodynamic (MHD) system:. 2. How to cite this paper: Yuan, Z.Q., Guo, L. and Lin, G.G. (2015) Inertial Manifolds for 2D Generalized MHD System. More results about inertial manifolds can be founded in [2]-[11]. We consider the following 2D generalized MHD system:. Where u is the fluid velocity field, v is the magnetic field, γ is the constant kinematic viscosity and η is the constant magnetic diffusivity. 2. This paper is organized as follows.

Preliminaries

Inertial Manifolds

T Φ p0