Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L2(T)
Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L2(T)
We consider the Cauchy problem for the 1-dimensional periodic cubic nonlinear Schrödinger (NLS) equation with initial data below L2. In particular, we exhibit nonlinear smoothing when the initial data are randomized. Then, we prove local well-posedness of the NLS equation almost surely for the initial data in the support of …