The Northern sky pulsar wind nebula 3C58 has been regarded as the
remnant of the SN1181, although radio expansion rate and optical
filaments velocity measurements suggest a larger age for this
nebula. We present two approaches for solving the transport equation
of particles in a convective wind. On the one hand, a 2D evolution
modeling employs the proper boundary conditions to explain the
measured radio velocity, the synchrotron nebular emission in terms of
photon index vs radius, synchrotron surface brightness and
terminating energy dependent size, as well as the inverse Compton $ \gamma$-ray flux. With this procedure we derive a nebular field
strength around 10 $\mu{G}$, which is well below the equipartition
value of 80 $\mu{G}$, with the strongest argument in favour of such a
weak field strength coming from a constraint on the cooling of the
highest energy electrons from the pulsar wind shock to allow X-ray
emitting electrons to survive to the edge of the pulsar wind nebula.
The SED distribution fails in reproduce the radio data. To overcome
this problem, a 1D time-dependent modeling is introduced, which successfully
reproduces the SED distribution. We predict the inverse Compton $ \gamma$-ray flux from 3C58 as a function of the system age, which
according to this time-dependent model, can be used by GLAST and ground-based
VHE gamma-ray observations in the northern hemisphere, such as MAGIC
and VERITAS, to shed light on the age problem.