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A continuous family of conserved energies for the Gross- Pitaevskii equation


Academic Report

Title: A continuous family of conserved energies for the  Gross- Pitaevskii equation

Reporter: Prof. Herbert Koch (University of Bonn)

Time: Sept 24, 2019 (Tuesday) PM 15:00-16:00

Location: A1101# room, Innovation Park Building

Contact: Prof. LI Junfeng (tel:84708351-1128)

Abstract: The Gross-Pitaevskii equation admits infinitely many formally conserved energies. I will present an extension to a continuous family of conserved energies, leading to uniform in time estimates in fractional and rough Sobolev spaces.

The brief introduction to the reporter: Herbert Koch is a professor at the Institute of Mathematics, University of Bonn, Germany, and an internationally renowned expert in harmonic analysis and differential equations. The main research fields include real harmonic analysis, long-term behavior of dispersion equation solutions, and well-posedness theory of fluid equation solutions. His and Daniel Tataru's results on the well-posedness of solutions to Navier-Stockes equations are landmark results in this field, which are called Koch-Tataru solutions in the international mathematical community. The dual space theory of bounded variation space introduced by them has become an important workspace for modern harmonic analysis and the theory of nonlinear dispersion equation. Many non-linear problems provide new approaches; their recent studies on the conservation law of dispersion equation provide a new and powerful method for the study of long-term behavior of solutions of dispersion equation. Professor Herbert Koch has published more than 80 papers in top mathematical journals, including Duke Math, Adv. Math. At the same time, Professor Koch is also the editor of Analysis & PDE, and SIAM Journal of Mathematical Analysis.