  Because pressure is determined globally for the incompressible Euler
equations, a localized change to the initial velocity will have an immediate
effect throughout space. For solutions to be physically meaningful, one would
expect such effects to decrease with distance from the localized change, giving
the solutions a type of stability. Indeed, this is the case for solutions
having spatial decay, as can be easily shown. We consider the more difficult
case of solutions lacking spatial decay, and show that such stability still
holds, albeit in a somewhat weaker form.
