题目：Nonrelativistic Limit of the Klein-Gordon Equations: Convergence Rates and Long Time Approximations

报告人：吕勇 教授 （南京大学）

时间：2023年10月19日 11:00-12:00

地点🤖👩‍🔧：腾讯会议室

摘要🗒：We study the nonrelativistic limit of the cubic Klein-Gordon equations. We show the cubic Klein-Gordon equation converges to the cubic Schr\"odinger equation with a convergence rate of order $\epsilon^{2}$. In particular for the defocusing case, for `smooth' initial data, we show error estimates of the form $(1+t)\epsilon^{2}$ at time $t$ which is valid up to long time of order $\epsilon^{-1}$; while for `nonsmooth' initial data, we show error estimates of the form $(1+t)\epsilon$ at time $t$ which is valid up to long time of order $\epsilon^{-\frac{1}{2}}$. These specific forms of error estimates coincide with the numerical results.

参会方式：腾讯会议室

账号：662-859-6692

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