On the Global Evolution of Vortex Filaments, Blobs, and Small Loops in 3D Ideal Flows
On the Global Evolution of Vortex Filaments, Blobs, and Small Loops in 3D Ideal Flows
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关于 3D 理想流中涡丝、斑点和小环的整体演化
DOI：
10.1007/s00220-006-0142-x
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发表时间：
2005
影响因子：
2.4
通讯作者：
M. Gubinelli
中科院分区：
文献类型：
--
作者：
L. Berselli;M. Gubinelli
我们考虑了一类广泛的近似模型的发展奇异分布的涡在三维不可压缩流体，我们表明，他们有整体光滑的解决方案。该证明利用了合适的哈密顿函数的存在性。我们分析的近似模型（基本上是离散和连续的涡丝和涡环）涉及到一些经典物理学的问题，有关湍流，也是非常高的雷诺数的流动的数值近似。最后，我们将我们的策略应用于数值方法中使用的细丝的离散模型。
We consider a wide class of approximate models of evolution of singular distributions of vorticity in three dimensional incompressible fluids and we show that they have global smooth solutions. The proof exploits the existence of suitable Hamiltonian functions. The approximate models we analyze (essentially discrete and continuous vortex filaments and vortex loops) are related to some problem of classical physics concerning turbulence and also to the numerical approximation of flows with very high Reynolds number. Finally, we apply our strategy to discrete models for filaments used in numerical methods.