The generic behavior of solutions to some evolution equations: asymptotics and Sobolev norms
Sergey A. Denisov
TL;DR
This paper investigates the typical long-term behavior of solutions to various evolution equations, with specific application to Schrödinger equations on the circle, focusing on asymptotic properties and Sobolev norms.
Contribution
It introduces a general framework for analyzing the asymptotic behavior of solutions to evolution equations, including Schrödinger equations on the circle, highlighting their generic properties.
Findings
Characterization of asymptotic behavior of solutions
Analysis of Sobolev norm growth over time
Application of methods to Schrödinger evolution on the circle
Abstract
We study generic behavior of solutions to a large class of evolution equations. The methods are applied to Schrodinger evolution on the circle.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Physics Problems · Gas Dynamics and Kinetic Theory · Advanced Mathematical Modeling in Engineering