23 citations · 38 across the 9 of their papers we have counts for
10 papers
Quantitative Scattering for the Energy-Critical Wave Equation on Asymptotically Flat Spacetimes
Benjamin Dodson, Sam Looi
We prove quantitative scattering for the three-dimensional defocusing energy-critical quintic wave equation on a class of asymptotically flat, possibly non-stationary perturbations…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1168
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients
Shi-Zhuo Looi, Ethan Sussman
Using the recent analysis of the output of the low-energy resolvent of Schrödinger operators on asymptotically conic manifolds (including Euclidean space) when the potential is sho…
A proof of Onsager's Conjecture for the SQG equation
Philip Isett, Shi-Zhuo Looi, Sam Looi
We construct solutions to the SQG equation that fail to conserve the Hamiltonian while having the maximal allowable regularity for this property to hold. This result solves the gen…
Improved decay for quasilinear wave equations close to asymptotically flat spacetimes including black hole spacetimes
Shi-Zhuo Looi
We study the quasilinear wave equation where the metric is close to and asymptotically approaches , which equals the Schwarzschild metric or…
Decay rates for cubic and higher order nonlinear wave equations on asymptotically flat spacetimes
Shi-Zhuo Looi
In this paper, we prove pointwise decay rates for cubic and higher order nonlinear wave equations, including quasilinear wave equations, on asymptotically flat and time-dependent s…
Pointwise decay for the energy-critical nonlinear wave equation
Shi-Zhuo Looi
This second article in a two-part series (following [arXiv:2105.02865], listed here as \cite{L}) proves optimal pointwise decay rates for the quintic defocusing wave equation with…
Global existence and pointwise decay for nonlinear waves under the null condition
Shi-Zhuo Looi, Mihai Tohaneanu
This paper proves global existence and sharp pointwise decay for solutions to nonlinear wave equations satisfying the semilinear null condition, on a class of three-dimensional, as…
Pointwise decay for the wave equation on nonstationary spacetimes
Shi-Zhuo Looi
The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave e…
Scattering for critical wave equations with variable coefficients
Shi-Zhuo Looi, Mihai Tohaneanu
We prove that solutions to the quintic semilinear wave equation with variable coefficients in scatter to a solution to the corresponding linear wave equation. The…