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Long‐Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation

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  • Jamel Benameur
  • Mongi Blel

Abstract

We study the behavior at infinity in time of any global solution θ∈𝒞(ℝ+,H.22-α(ℝ2)) of the surface quasigeostrophic equation with subcritical exponent 2/3 ≤ α ≤ 1. We prove that lim t→∞∥θ(t)∥H.22-α=0. Moreover, we prove also the nonhomogeneous version of the previous result, and we prove that if θ∈𝒞(ℝ+,H.22-α(ℝ2)) is a global solution, then lim t→∞∥θ(t)∥H22-α=0.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:627813
DOI: 10.1155/2012/627813
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