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홈 > 학술정보 >학술행사 > 세미나
KAIST 수리과학과 세미나

Title
Fourier restriction norm method for Schrödinger waves
Speaker
권순식   (KAIST )
Date
2017-01-03 14:00:00
Host
KAIST
Place
자연과학동 2411
Abstract
Fourier restriction norm method, more precisely X^{s,b} spaces introduced by Bourgain, was an efficient tool for low regularity problems of nonlinear dispersive equations. In the well-posedness problems, we are often interested in proving multilinear estimates in X^{s,b} spaces. These estimates are in turn reduced to weighted convolution estimates of L^2 functions. In [Ta], Tao systematically studies this type of weighted L^2 convolution estimates. In the lectures, I will roughly follow [Ta]. After introducing preliminary reduction and fundamental tools, I will cover some selected topics toward the orthogonal interaction of Schrödinger waves. Although this is motivated by a well-posedness problem in PDEs, I will mostly focus on desired bilinear estimates of harmonic analytic nature. I will assume familiarity to Fourier transform and Littlewood-Paley decomposition. (In particular, MAS 640 is sufficient.) [Ta] T. Tao, Multilinear weighted convolution of L^2 functions and applications to nonlinear dispersive equations, Amer. J. Math. 123(2001), 839-908.
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