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Faculty of Science Mathematics & Statistics
Faculty of Science

Mathematics & Statistics

PDE/Analysis Seminar - "Global well-posedness in the derivative NLS equation", Jiaqi Liu

From November 24, 2017 13:30 until November 24, 2017 14:30
At HH/410

 


Jiaqi Liu
University of Toronto

Title:  Global well-posedness in the derivative NLS equation

Abstract:   We study the Derivative Nonlinear Schroedinger equation for generic initial conditions in weighted Sobolev spaces that can support finitely bright solitons (but excluding spectral singularities). We prove global well-posedness and give a full description of the long- time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. We use the nonlinear steepest descent method of Deift and Zhou complemented by the recent work of Borghese-Jenkins-McLaughlin on soliton resolution for the focusing nonlinear Schroedinger equation.

 

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McMaster University - Faculty of Science

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Department of Mathematics & Statistics
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1280 Main Street West
Hamilton, Ontario, Canada
L8S 4K1

Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.27034
Undergrad Email Inquiries:
undergrad@math.mcmaster.ca

McMaster University - Faculty of Science

Mailing Address

Department of Mathematics & Statistics
McMaster University

Hamilton Hall, Room 218
1280 Main Street West
Hamilton, Ontario, Canada
L8S 4K1

Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.27034
Undergrad Email Inquiries:
undergrad@math.mcmaster.ca