Linear and nonlinear wave equation -- with applications to general relativity
I will present a vector field method approach to establishing properties of solutions of wave equations. The goal is to reach topics such as the proof of (almost) sharp estimates for linear waves on black hole backgrounds and the presentation of certain results concerning the black hole stability in spherical symmetry.
日期
2025年09月15日 至 -
课程大纲
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)
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)
参考资料
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
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
听众
Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
公开
笔记公开
公开
语言
英文