Asymptotic stability of the critical and super-critical dissipative quasi-geostrophic equation

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Published 13 November 2006 • 2006 IOP Publishing Ltd and London Mathematical Society
, , Citation Bo-Qing Dong and Zhi-Min Chen 2006 Nonlinearity 19 2919 DOI 10.1088/0951-7715/19/12/011

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Author affiliations

1 School of Mathematical Sciences, Nankai University, Tianjin 300071, People's Republic of China

2 School of Engineering Sciences, Ship Science, University of Southampton, Southampton SO17 1BJ, UK

Dates

  1. Received 27 May 2006
  2. Published

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0951-7715/19/12/2919

Abstract

The asymptotic stability for the weak solution θ of the critical and supercritical dissipative quasi-geostrophic equation in the Serrin-type class ∇θ ∊ Lr(0, ∞;Lp(R2)) is examined. This equation is perturbed by large initial data and external functions. It is shown that every weak perturbed solution has the same asymptotic behaviour as that of θ. More precisely, the difference decays in the norm of L2(R2).

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10.1088/0951-7715/19/12/011