The APDE seminar on Monday, 3/17, will be given by Rana Badreddine (UCLA) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Robert Schippa ().

Title: The Calogero-Moser derivative NLS equation

Abstract: We consider a type of nonlocal nonlinear derivative Schrödinger equation on the torus, called the Calogero-Sutherland DNLS equation.We derive an explicit formula to the solution of this nonlinear PDE. Moreover, using the integrability tools, we establish the global well-posedness of this equation in all the Hardy-Sobolev spaces \(H^s_+(\mathbb{T}), s\geq0\) down to the critical regularity space, and under a mass assumption on the initial data for the focusing equation, and for arbitrary initial data for the defocusing equation. Finally, a sketch of the proof for extending the flow to the critical regularity \(L^2_+(\mathbb{T})\) will be presented.