Continuous dependence on initial data
= Continuous dependence on initial data
Continuous dependence means that convergence of the initial data in a specified topology implies convergence of the corresponding solutions in the specified solution topology. It is a stability requirement, not merely existence or uniqueness. <Smooth-data instability of the Cauchy-Riemann Cauchy problem> gives a counterexample even when the initial data converge uniformly with every fixed number of derivatives.