Linear and nonlinear wave equations —with applications to general relativity

Speaker

Yannis Angelopoulos

Associate Professor of BIMSA

Time

Mon.& Tues., 9:50-11:25 am,

Sept. 15-Dec. 9, 2025

Venue

C654, Shuangqing Complex Building A

Online

Zoom Meeting ID: 276 366 7254

Passcode: YMSC

Description

Contents:

1) Basic facts and estimates for solutions of linear wave equations on Minkowski

2) Introduction to the vector field method

3) Basic energy estimates using the vector field method on Minkowski

4) The r^p method of Dafermos and Rodnianski

5) Small data global well-posedness for nonlinear wave equations on Minkowski

6) Energy decay and pointwise decay for linear waves on black hole spacetimes*

7) Stability of black holes for the Einstein equations under spherical symmetry (if time permits)

*First goal is to cover subextremal black hole spacetimes, if time permits we will cover some extremal cases too.

References:

1) "Introduction to nonlinear wave equations", Jonathan Luk, https://web.stanford.edu/~jluk/NWnotes.pdf

2) "Lecture Notes, PDE", Sigmund Selberg

3) "Lectures on black holes and linear waves", Mihalis Dafermos and Igor Rodnianski, http://www.arxiv.org/abs/0811.0354

4) "A new physical-space approach to decay for the wave equation with applications to black hole spacetimes", Mihalis Dafermos and Igor Rodnianski, https://arxiv.org/abs/0910.4957

5) "Global solutions of nonlinear wave equations in time dependent inhomogeneous media", Shiwu Yang, https://arxiv.org/abs/1010.4341

6) "A vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary spacetimes", Yannis Angelopoulos, Stefanos Aretakis, Dejan Gajic, https://arxiv.org/abs/1612.01565