Invariant Gibbs measures of the energy for shell models of turbulence: the inviscid and viscous cases

Invariant Gibbs measures of the energy for shell models of turbulence: the inviscid and viscous cases
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湍流壳模型能量的不变吉布斯测度：无粘性和粘性情况

DOI：
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发表时间：
2011
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影响因子：
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通讯作者：
B. Ferrario
B. Ferrario
中科院分区：
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文献类型：
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作者：
H. Bessaih;B. Ferrario

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吉布斯型高斯测度与某些湍流壳模型相关；它们是通过能量构建的，能量是 3D 无粘性非受力壳模型的守恒量。我们证明了随机粘性壳模型存在唯一的全局流，其吉布斯测度对于该流是不变的。此外，我们证明确定性无粘壳模型对于这些措施具有平稳解。
Gaussian measures of Gibbsian type are associated with some shell model of turbulence; they are constructed by means of the energy, a conserved quantity for the 3D inviscid and unforced shell model. We prove the existence of a unique global flow for a stochastic viscous shell model with the property that these Gibbs measures are invariant for this flow. Moreover, we prove that the deterministic inviscid shell model has a stationary solution with respect to these measures.