Louise Gassot: Cauchy Problem in Low Regularity for Schrödinger-Type Equations

Abstract:

This is a collaboration with Nicolas Camps. We are interested in the Schrödinger equation in the supercritical regime, for which the Cauchy problem is ill-posed. Ill-posedness manifests as a growth of norms in arbitrarily short times. We show that this phenomenon persists when we restrict the initial data’s regularization to convolution only. This result will be compared to the study of the local well-posedness for the same equation with random initial data. Finally, in collaboration with Rémi Carles, we adapt this strategy to explain the loss of regularity of the flow.