A dyadic model on a tree
A dyadic model on a tree
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树上的二元模型
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
F. Morandin
中科院分区：
文献类型：
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作者：
D. Barbato;L. Bianchi;F. Flandoli;F. Morandin
我们研究耦合在树状结构中的非线性微分方程的无限系统。该系统之前已在文献中介绍过，并且是湍流二元壳模型的衍生模型。它在小波分解的粗略近似中模仿 3D 欧拉和纳维-斯托克斯方程。我们证明了有限能量解的存在性、无粘性非受迫情况下的反常耗散、受迫情况下稳态解（保守或非保守）的存在性和唯一性。
We study an infinite system of nonlinear differential equations coupled in a tree-like structure. This system was previously introduced in the literature and it is the model from which the dyadic shell model of turbulence was derived. It mimics 3D Euler and Navier-Stokes equations in a rough approximation of wavelet decomposition. We prove existence of finite energy solutions, anomalous dissipation in the inviscid unforced case, existence and uniqueness of stationary solutions (either conservative or not) in the forced case.