On One-dimension Quasilinear Wave Equations with Null Conditions
Time: 2019-09-19
Published By: He Liu
Speaker(s): Dongbing Zha (Donghua University)
Time: 16:00-17:00 September 24, 2019
Venue: Room 29, Quan Zhai, BICMR
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.
