  This article concerns the formation of finite-time singularities in solutions
to quasilinear hyperbolic systems with small initial data. By constructing a
special test function, we first present a simpler proof of the main result in
Sideris' "Formation of singularities in three-dimensional compressible fluids":
the global classical solution is non-existent for compressible Euler equation
even for some small initial data. Then we apply this approach to nonlinear
elastodynamics and magnetohydrodynamics, showing that the classical solutions
to these equations can still blow up in finite time even if the initial data is
small enough.
