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Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball II: the 3d case

Jean Bourgain; Aynur Bulut — 2014

Journal of the European Mathematical Society

We extend the convergence method introduced in our works [8–10] for almost sure global well-posedness of Gibbs measure evolutions of the nonlinear Schrödinger (NLS) and nonlinear wave (NLW) equations on the unit ball in $ℝ^{d}$ to the case of the three dimensional NLS. This is the first probabilistic global well-posedness result for NLS with supercritical data on the unit ball in $ℝ^{3}$ . The initial data is taken as a Gaussian random process lying in the support of the Gibbs measure associated to the equation,...

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