Probabilistic Cauchy theory for the mass-critical fourth-order nonlinear Schrödinger equation

Journal of Mathematical Physics, Volume 62, Issue 3, March 2021. We consider the mass-critical nonlinear fourth-order Schrödinger equations with random initial data. We prove almost sure local well-posedness and probabilistic small data global well-posedness below L2-space. We also prove probabilistic blow-up for the equation with non-gauge invariance and rough random initial data.