[M1 Seminar II] Week 6 : Weighted a priori Estimates for Small Data

For the proof of the global existence theorem of nonlinear wave equations, this a priori estimates is essential as well as the high energy estimates. Also the high energy estimates play an important role in the proof of a priori … Continue reading

[M1 Seminar] Week 13 : Elementary Inequalities on the Klainerman Vector Field

We construct the Klainerman vector field with some operators which were defined in the last seminar. And we prove some basic inequalities of these family of operators which play an important role for our final goal. M1_Semi_Week13  

[M1 Seminar] Week 5 : Energy Estimates for the Linear Symmetric Hyperbolic System

We derive the corresponding estimates for higher derivatives from the basic energy estimates which was given in the last week. We also prove a simple corollary using this result. And we discuss about the finite propagation speed of the hyperbolic … Continue reading