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：beat365中国在线体育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.