Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Looi, Shi-Zhuo"'
Autor:
Looi, Shi-Zhuo, Sussman, Ethan
Using the recent analysis of the output of the low-energy resolvent of Schr\"odinger operators on asymptotically conic manifolds (including Euclidean space) when the potential is short-range, we produce detailed asymptotic expansions for the solution
Externí odkaz:
http://arxiv.org/abs/2407.20991
Autor:
Looi, Shi-Zhuo, Xiong, Haoren
We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. For cubic nonlinearities $a(t,x)\phi^3$, we prove $\phi(t, x) = 2c t^{-2} + O(t^{-3+})$ in compact
Externí odkaz:
http://arxiv.org/abs/2407.08997
Autor:
Looi, Shi-Zhuo, Isett, Philip
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 generalized Onsager conjecture on the threshold regularity for Hamiltonia
Externí odkaz:
http://arxiv.org/abs/2407.02578
Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We offer a mathem
Externí odkaz:
http://arxiv.org/abs/2310.04444
Autor:
Looi, Shi-Zhuo
We study the quasilinear wave equation $\Box_{g}\phi=0$ where the metric $g = g(\phi,t,x)$ is close to and asymptotically approaches $g(0,t,x)$, which equals the Schwarzschild metric or a Kerr metric with small angular momentum, as time tends to infi
Externí odkaz:
http://arxiv.org/abs/2208.05439
Autor:
Looi, Shi-Zhuo
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 spacetimes. We assume that the solution to the linear equation (rather
Externí odkaz:
http://arxiv.org/abs/2207.10280
Autor:
Looi, Shi-Zhuo
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 large initial data on nonstationary spacetimes, and both the quintic d
Externí odkaz:
http://arxiv.org/abs/2205.13197
Autor:
Looi, Shi-Zhuo, Tohaneanu, Mihai
We study the nonlinear wave equation with the null condition and small initial data on nonstationary spacetimes. Under the assumption that the solution to the linear equation satisfies local energy bounds, we prove global existence of solutions, and
Externí odkaz:
http://arxiv.org/abs/2204.03626
Autor:
Looi, Shi-Zhuo
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 equation with variable coefficients in $\mathbb R^{1+3}$, first-order t
Externí odkaz:
http://arxiv.org/abs/2105.02865
Autor:
Looi, Shi-Zhuo, Tohaneanu, Mihai
We prove that solutions to the quintic semilinear wave equation with variable coefficients in $\mathbb R^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to\infty$, but are allowed t
Externí odkaz:
http://arxiv.org/abs/1912.06795