2013 Fiscal Year Final Research Report
Solvability and asymptotic behavior of solution for stochastic nonlinear dispersive equations
| Project/Area Number |
23654051
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
TSUTSUMI YOSHIO 京都大学, 理学(系)研究科(研究院), 教授 (10180027)
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| Research Collaborator |
BOUARD Anne De パリ理工科学校
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| Project Period (FY) |
2011 – 2013
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| Keywords | 確率非線形分散型方程式 / Gibbs測度 / Kuksin流の不変測度 / 等温Falkモデル / 加法的ノイズ付きZkharov方程式 / 電離層における電磁場擾乱 / 時間大域解の存在 |
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| Research Abstract |
If the scale or the measure is appropriately chosen, the volume of flows generated by evolution equations can be conserved. Such a measure is called an invariant measure. It is very important to construct an invariant measure, because the global behavior of solutions for nonlinear evolution equations can be investigated in view of the invariant measure. We have constructed two kinds of invariant measures, that is, the Gibbs measure and the measure proposed by Kuksin. We also have copared those two invariantmeasures. Furthermore, we have studied the Zakharov equations with additive noises, which is a mathematical model to describe a turbulence of spectrums of electromagnetic waves in the ionosphere. We have proved the global existence in time of solutions for the Cauchy problem of the Zakharove equations with additive noises.
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