The global attractors for the dissipative generalized Hasegawa-Mima equation
type: Item
instance of: scholarly article
title: The global attractors for the dissipative generalized Hasegawa-Mima equation
zbMATH Open document ID: 1156.35334
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2008-05-26T00:00:00Z
review text: In this paper the following periodic initial value problem of the generalized Hasegawa-Mima equation with dissipative term \[ u_t-\Delta u_t- k_n u_y+ \gamma(u-\Delta u)+ f(u)_x+ h(u)= \{u,\Delta u\}+ g(x,y), \] \[ u(x,y,0)= u_0(x, y),\quad (x,y)\in \Omega= (0,2M)\times (0,2M), \] \[ u(x+ 2M, y+ 2M,t)= u(x,y,t),\quad t> 0, \] is considered. There \(\gamma\) and \(k_n\) are positive constants, \(\{f,g\}= (\partial_x f)(\partial_y g)- (\partial_y f)(\partial_x g)\), \(u(x,y, t)\) is an unknown real-valued function, \(f\), \(h\) and \(g\) are given real valued functions, \(f,h\in C^\infty\), \(g\in L^2(\Omega)\). First, the \(t\)-independent a priori estimates for the solutions are established. Then the existence of the global attractor of the periodic initial value problem is proved. Further, the estimates of the Hausdorff and fractal dimensions for the global attractor are given.
reviewed by: A. Cichocka
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 5278770
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: fractal dimension
zbMATH Keywords: periodic initial value problem
author: Ruifeng Zhang
MaRDI profile type: Publication
full work available at URL: s10255-004-4131-9
OpenAlex ID: W2168276618
cites work: Q4514557
cites work: Q5520962
cites work: Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time
cites work: Existence and uniqueness of global solution of the Hasegawa–Mima equation
cites work: Pseudo-three-dimensional turbulence in magnetized nonuniform plasma
cites work: Global attractor for Hasegawa-Mima equation
DOI: 10.1007/S10255-004-4131-9
description: scientific article; zbMATH DE number 5278770