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 Hamilto- nian functions. The approximate models we analyze (essentially discrete and continuous vortex ﬁlaments and vortex loops) are related to some problem of classical physics con- cerning 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.
|Autori:||Berselli, Luigi Carlo; Gubinelli, M.|
|Titolo:||On the global evolution of vortex filaments, blobs, and small loops in 3D ideal flows|
|Anno del prodotto:||2007|
|Digital Object Identifier (DOI):||10.1007/s00220-006-0142-x|
|Appare nelle tipologie:||1.1 Articolo in rivista|