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.
Liu,On the probabilistic well-posedness of the two-dimensional periodic nonlinear Schr¨ odinger equation with the quadratic nonlinearity|u| 2, J
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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.