  We study the regularity of sonic curves to a two-dimensional Riemann problem
for the nonlinear wave system of Chaplygin gas, which is an essential step for
the global existence of solutions to the two-dimensional Riemann problems. As a
result, we establish the global existence of uniformly smooth solutions in the
semi-hyperbolic patches up to the sonic boundary, where the degeneracy of
hyperbolicity occurs. Furthermore, we show the C^1 regularity of sonic curves.
