| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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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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