Following our previous results on this subject \cite{PRA29, PRA30, PRA33, PRA34}, integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of {\em integral charecteristic numbers} of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy data. Global solutions of variational problems constrained by $(NS)$ are classified by means of suitable integral bordism groups too.
Geometry of PDE's. IV: Navier-Stokes equation and integral bordism groups / Prastaro, Agostino. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 2:338(2008), pp. 1140-1151. [10.1016/j.jmaa.2007.06.009]
Geometry of PDE's. IV: Navier-Stokes equation and integral bordism groups
PRASTARO, Agostino
2008
Abstract
Following our previous results on this subject \cite{PRA29, PRA30, PRA33, PRA34}, integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of {\em integral charecteristic numbers} of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy data. Global solutions of variational problems constrained by $(NS)$ are classified by means of suitable integral bordism groups too.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
