  In this paper, we study the Cauchy problem with decaying initial data for the
nonlocal modified Korteweg-de Vries equation (nonlocal mKdV)
  \[q_t(x,t)+q_{xxx}(x,t)-6q(x,t)q(-x,-t)q_x(x,t)=0,\]
  which can be viewed as a generalization of the local classical mKdV equation.
We first formulate the Riemann-Hilbert problem associated with the Cauchy
problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear
steepest-descent method to analyze the long-time asymptotics for the solution
of the nonlocal mKdV equation. In contrast with the classical mKdV equation, we
find some new and different results on long-time asymptotics for the nonlocal
mKdV equation and some additional assumptions about the scattering data are
made in our main results.
