Towards a sufficient criterion for collapse in 3D Euler equations

A sufficient integral criterion for a blow-up solution of the Hopf equations (the Euler equations with zero pressure) is found. This criterion shows that a certain positive integral quantity blows up in a finite time under specific initial conditions. Blow-up of this quantity means that solution of the Hopf equation in 3D can not be continued in the Sobolev space $H^2({\cal R}^3)$ for infinite time

High energy neutrino absorption by W production in a strong magnetic field

An influence of a strong external magnetic field on the neutrino self-energy operator is investigated. The width of the neutrino decay into the electron and W boson, and the mean free path of an ultra-high energy neutrino in a strong magnetic field are calculated. A kind of energy cutoff for neutrinos propagating in a strong field is defined.Comment: 13 pages, LaTeX, 1 EPS figure, submitted to Physics Letters