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

 Title: Nonrelativistic limit of the Klein-Gordon equations: convergence rates and long time approximations Speaker: 吕勇 教授，南京大学 Inviter: 王勇 副研究员 Time & Venue: 2023.3.15 9:00 N613 Abstract: 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. Affiliation:

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