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【10月21日】吕勇学术报告

发布时间:2023-10-19文章来源:威廉希尔中文网站张艳华 浏览次数:

报告题目:Nonrelativistic limit of the Klein-Gordon equations: convergence rates and long time approximations

报告人:吕勇

报告时间:2023.10.21 16:30-17:30

报告地点:威廉希尔中文网站301

报告摘要: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.


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