| Asymptotic Smoothing Effect of Solutions to Davey-Stewartson Systems on the Whole Plane |
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| 作者姓名： | Cai Di ZHAO Yong Sheng LI Sheng Fan ZHOU |
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| 作者单位： | [1]School of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, P. R. China [2]Department of Mathematical Sciences,South China University of Technology, Guangdong, 510640, P. R. China [3]Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China |
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| 基金项目： | This work is supported by Natural Science Foundation of China under grant numbers 10471047 and 10471086, is also supported by Zhejiang Province Natural Science Foundation with item M103043 and Natural Science Foundation of Guangdong Province of China under grant No. 004020077; Acknowledgments The corresponding author thanks Professor Zhengyi Lu for his constant supports and encouragements. |
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| 摘 要： | This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R^2. Making use of the Fourier spectral projector, together with a long time comparison between the solutions to the Davey-Stewartson systems and to an auxiliary problem, we prove that the global attractor in H^1 （R^2） for the addressed Davey-Stewartson systems is a compact subset of H^2（R^2）, and thus reveal the asymptotic smoothing effect of the solutions for the systems.
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| 关 键 词： | Davey-Stewartson系统 渐近平滑作用 全局吸引子 渐近解 |
| 收稿时间： | 19 December 2005 |
| 修稿时间： | 2005-12-19 |
Asymptotic Smoothing Effect of Solutions to Davey–Stewartson Systems on the Whole Plane |
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| Cai Di ZHAO Yong Sheng LI Sheng Fan ZHOU.Asymptotic Smoothing Effect of Solutions to Davey-Stewartson Systems on the Whole Plane[J].Acta Mathematica Sinica,2007,23(11):2043-2060. |
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| Authors: | Cai Di Zhao Yong Sheng Li Sheng Fan Zhou |
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| Institution: | (1) School of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, P. R. China;(2) Department of Mathematical Sciences, South China University of Technology, Guangdong, 510640, P. R. China;(3) Department of Applied Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. China |
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| Abstract: | This paper discusses the Cauchy problem of elliptic-elliptic-type Davey–Stewartson systems
with zero-order dissipation on ℝ2. Making use of the Fourier spectral projector, together with a long
time comparison between the solutions to the Davey–Stewartson systems and to an auxiliary problem,
we prove that the global attractor in H
1(ℝ2) for the addressed Davey–Stewartson systems is a compact
subset of H
2(ℝ2), and thus reveal the asymptotic smoothing effect of the solutions for the systems.
This work is supported by Natural Science Foundation of China under grant numbers 10471047 and 10471086, is also supported
by Zhejiang Province Natural Science Foundation with item M103043 and Natural Science Foundation of Guangdong Province of
China under grant No. 004020077 |
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| Keywords: | Davey-Stewartson systems asymptotic smoothing effect global attractor zero-order dissipation |
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