Renormalized BBM with rough Gaussian initial data converges in law to stochastic BBM forced by derivative of spatial white noise, for all regularities alpha <= 1/4.
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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Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation
Renormalized BBM with rough Gaussian initial data converges in law to stochastic BBM forced by derivative of spatial white noise, for all regularities alpha <= 1/4.