On One-dimension Quasilinear Wave Equations with Null Conditions
发布时间：2019年09月19日
浏览次数：6495
发布者: He Liu
主讲人： Dongbing Zha (Donghua University)
活动时间： 从 2019-09-24 16:00 到 17:00
场地： 北京国际数学研究中心，全斋全29教室
In this talk, we will show that one-dimension systems of quasilinear wave equations with null conditions admit global classical solutions for small initial data. This result extends Luli, Yang and Yu's seminal work [G.K.Luli, S.Yang, P.Yu, On one-dimension semi-linear wave equations with null conditions}, Adv. Math. 329 (2018) 174--188] from the semilinear case to the quasilinear case. Furthermore, we also prove that the global solution is asymptotic free in the energy sense. In order to achieve these goals, we first carefully design some energy norms to display the quasilinear null structure, then employ Luli, Yang and Yu's weighted energy estimates with positive weights, introduce some space-time weighted energy estimates and pay some special attentions to the highest order energies, finally use some suitable bootstrap process to close the argument.
