The paper defines enhanced probabilistic well-posedness by imposing stability at the origin and reinterprets recent 'beyond variance blowup' results for dispersive PDEs as probabilistic ill-posedness.
Hadamard,Lectures on Cauchy’s Problem in Linear Partial Differential Equations.New Haven: Yale University Press; London: Humphrey Milford; Oxford: University Press
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On probabilistic ill-posedness
The paper defines enhanced probabilistic well-posedness by imposing stability at the origin and reinterprets recent 'beyond variance blowup' results for dispersive PDEs as probabilistic ill-posedness.