  Globally conserved phase ordering dynamics is investigated in systems with
short range correlations in the initial condition. A Ginzburg-Landau equation
with a global conservation law is employed as the phase field model. The
conditions are found under which the sharp-interface limit of this equation is
reducible to the area-preserving motion by curvature. Numerical simulations
show that, for both critical and off-critical quench, the equal time pair
correlation function exhibits dynamic scaling, and the characteristic
coarsening length obeys a power law in time with a 1/2 exponent. For the
critical quench, our results are in excellent agreement with earlier results.
For off-critical quench (Ostwald ripening) we investigate the dynamics of the
size distribution function of the minority phase domains. The simulations show
that, at large times, this distribution function has a self-similar form with
growth exponent 1/2. The scaled distribution, however, strongly differs from
the classical Wagner distribution. We attribute this difference to coalescence
of domains. A new theory of Ostwald ripening is developed that takes into
account binary coalescence events. The theoretical scaled distribution function
agrees very well with that obtained in the simulations.
