Periodic nonlinear Schrödinger equation with distributional potential and invariant measures
arxiv(2024)
Abstract
In this paper, we continue some investigations on the periodic NLSE started
by Lebowitz, Rose and Speer and by Bourgain with the addition of a
distributional multiplicative potential. We prove that the equation is globally
wellposed for a set of data of full normalized Gibbs measure, after suitable
truncation in the focusing case. The set and the measure are invariant under
the flow. The main ingredients used are Strichartz estimates on periodic NLS
with distributional potential to obtain local well-posedness for low regularity
initial data.
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