A mathematical model of solar flares.

The phenomenon of solar flares is modeled assuming that the magnetic field is force-free and that its evolution is quasi-static. This model is simplified so as to be tractable and yields a semi-linear elliptic equation in a half-plane depending on a parameter lambda which describes the time evolution. It is proved that there are (at least) two branches of solutions which have distinct asymptotic behaviors at infinity. The upper branch exists for all lambda greater than 0, but the lower branch exists only on a finite interval /0, lambda exp c/. As stable solutions must have the same asymptotic behavior as the lower branch of solutions, and as this is impossible after lambda exp c, it is contended that no stable solution exists after lambda exp c and that a solar flare is thus triggered.