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

Jamel Benameur and Mongi Blel

Abstract and Applied Analysis, 2012, vol. 2012, 1-12

Abstract:

We study the behavior at infinity in time of any global solution 𠜃 ∈ ð ’ž ( â„ + , ̇ ð » 2 − 2 ð ›¼ ( â„ 2 ) ) of the surface quasigeostrophic equation with subcritical exponent 2 / 3 ≤ ð ›¼ ≤ 1 . We prove that l i m ð ‘¡ → ∞ ‖ 𠜃 ( ð ‘¡ ) ‖ ̇ ð » 2 − 2 ð ›¼ = 0 . Moreover, we prove also the nonhomogeneous version of the previous result, and we prove that if 𠜃 ∈ ð ’ž ( â„ + , ̇ ð » 2 − 2 ð ›¼ ( â„ 2 ) ) is a global solution, then l i m ð ‘¡ → ∞ ‖ 𠜃 ( ð ‘¡ ) ‖ ð » 2 − 2 ð ›¼ = 0 .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:627813

DOI: 10.1155/2012/627813

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