  We present a micromagnetic theory of compact magnetic skyrmions under applied
magnetic field that accounts for the full dipolar energy and the interfacial
Dzyaloshinskii-Moryia interaction (DMI) in the thin film regime. Asymptotic
analysis is used to derive analytical formulas for the parametric dependence of
the skyrmion size and rotation angle, as well as the energy barriers for
collapse and bursting, two processes that lead to a finite skyrmion lifetime.
We demonstrate the existence of a new regime at low DMI, in which the skyrmion
is stabilized by a combination of non-local dipolar interaction and a magnetic
field applied parallel to its core, and discuss the conditions for an
experimental realization of such field-stabilized skyrmions.
