Dynamics of quintic nonlinear Schrödinger equations in 𝐻^{2/5⁺}(𝕋)
Joackim Bernier, Benoît Grébert, Tristan Robert
Source abstract
In this paper, we succeed in integrating Strichartz estimates (encoding the dispersive effects of the equations) in Birkhoff normal form techniques. As a consequence, we deduce a result on the long time behavior of quintic NLS solutions on the circle for small but very irregular initial data (in H s ( T ) H^s(\mathbb {T}) for s > 2 / 5 s>2/5 ). Note that since 2 / 5 > 1 2/5>1 we cannot claim conservation of energy and, more importantly, since 2 / 5 > 1 / 2 2/5>1/2 , we must dispense with the algebra property of H s H^s . This is the first dynamical result where we use the dispersive properties of NLS in a context of Birkhoff normal form.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.