Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation
We study the behavior at infinity in time of any global solution θ∈C(R+,Ḣ2-2α(R2)) of the surface quasigeostrophic equation with subcritical exponent 2/3≤α≤1. We prove that limt→∞∥θ(t)∥Ḣ2-2α=0. Moreover, we prove also the nonhomogeneous version of the previous result, and we prove that if θ∈C(R+,...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/627813 |
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| author | Jamel Benameur Mongi Blel |
| author_facet | Jamel Benameur Mongi Blel |
| author_sort | Jamel Benameur |
| collection | DOAJ |
| description | We study the behavior at infinity in time of any global solution θ∈C(R+,Ḣ2-2α(R2)) of the surface quasigeostrophic equation with subcritical exponent 2/3≤α≤1. We prove that limt→∞∥θ(t)∥Ḣ2-2α=0. Moreover, we prove also the nonhomogeneous version of the previous result, and we prove that if θ∈C(R+,Ḣ2-2α(R2)) is a global solution, then limt→∞∥θ(t)∥H2-2α=0. |
| format | Article |
| id | doaj-art-36435d07160940ecbdac062dff8e6176 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-36435d07160940ecbdac062dff8e61762025-02-03T06:07:52ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/627813627813Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic EquationJamel Benameur0Mongi Blel1Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaWe study the behavior at infinity in time of any global solution θ∈C(R+,Ḣ2-2α(R2)) of the surface quasigeostrophic equation with subcritical exponent 2/3≤α≤1. We prove that limt→∞∥θ(t)∥Ḣ2-2α=0. Moreover, we prove also the nonhomogeneous version of the previous result, and we prove that if θ∈C(R+,Ḣ2-2α(R2)) is a global solution, then limt→∞∥θ(t)∥H2-2α=0.http://dx.doi.org/10.1155/2012/627813 |
| spellingShingle | Jamel Benameur Mongi Blel Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation Abstract and Applied Analysis |
| title | Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation |
| title_full | Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation |
| title_fullStr | Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation |
| title_full_unstemmed | Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation |
| title_short | Long-Time Decay to the Global Solution of the 2D Dissipative Quasigeostrophic Equation |
| title_sort | long time decay to the global solution of the 2d dissipative quasigeostrophic equation |
| url | http://dx.doi.org/10.1155/2012/627813 |
| work_keys_str_mv | AT jamelbenameur longtimedecaytotheglobalsolutionofthe2ddissipativequasigeostrophicequation AT mongiblel longtimedecaytotheglobalsolutionofthe2ddissipativequasigeostrophicequation |