Zobrazeno 1 - 10
of 46
pro vyhledávání: '"Wong, Willie Wai Yeung"'
Publikováno v:
Mathematical Research Letters 2023
We prove global well-posedness of the initial value problem for a class of variational quasilinear wave equations, in one spatial dimension, with initial data that is not-necessarily small. Key to our argument is a form of quasilinear null condition
Externí odkaz:
http://arxiv.org/abs/1912.04692
Autor:
Wong, Willie Wai Yeung
Building on the hyperboloidal foliation approach of Lefloch and Ma, we extend Klainerman's physical-space approach to dispersive estimates to recover the frequency-restricted $L^1$--$L^\infty$ dispersive estimates for Klein-Gordon equations. The hype
Externí odkaz:
http://arxiv.org/abs/1909.05956
Publikováno v:
Trans. of AMS, Volume 374, Number 2, February 2021, Pages 773--802
We prove global, or space-time weighted, versions of the Gagliardo-Nirenberg interpolation inequality, with $L^p$ ($p < \infty$) endpoint, adapted to a hyperboloidal foliation. The corresponding versions with $L^\infty$ endpoint was first introduced
Externí odkaz:
http://arxiv.org/abs/1903.12129
Publikováno v:
Forum of Mathematics, Pi 8 (2020) e13
We prove that any simple planar travelling wave solution to the membrane equation in spatial dimension $d \geq 3$ with bounded spatial extent is globally nonlinearly stable under sufficiently small compactly-supported perturbations, where the smallne
Externí odkaz:
http://arxiv.org/abs/1903.03553
Autor:
Wong, Willie Wai Yeung
We prove the small-data global existence for the wave-map equation on $\mathbb{R}^{1,2}$ using a variant of the vector field method. The main innovations lie in the introduction of two new linear estimates. First is the control of the dispersive deca
Externí odkaz:
http://arxiv.org/abs/1712.07684
Autor:
An, Xinliang, Wong, Willie Wai Yeung
Publikováno v:
Class. Quantum Gravity 35, 025011 (2018)
Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian base and arbitrary dimensional Riemannian fibers. We first give a syst
Externí odkaz:
http://arxiv.org/abs/1707.01483
Autor:
Wong, Willie Wai Yeung
Publikováno v:
Archiv der Mathematik, 110(3), 273-289 (2018)
We prove the pointwise decay of solutions to three linear equations: (i) the transport equation in phase space generalizing the classical Vlasov equation, (ii) the linear Schrodinger equation, (iii) the Airy (linear KdV) equation. The usual proofs us
Externí odkaz:
http://arxiv.org/abs/1701.01460
Autor:
Wong, Willie Wai-Yeung
Publikováno v:
J. Hyperbolic Differential Equations (2018)
We prove that there does not exist global-in-time axisymmetric solutions to the time-like minimal submanifold system in Minkowski space. We further analyze the limiting geometry as the maximal time of existence is approached.
Externí odkaz:
http://arxiv.org/abs/1607.06846
Autor:
Wong, Willie Wai Yeung
Publikováno v:
Proc. Amer. Math. Soc. Ser. B 4 (2017), 47-52
In a 2004 paper, Lindblad demonstrated that the minimal surface equation on $\mathbb{R}l^{1,1}$ describing graphical time-like minimal surfaces embedded in $\mathbb{R}^{1,2}$ enjoy small data global existence for compactly supported initial data, usi
Externí odkaz:
http://arxiv.org/abs/1601.01096
Autor:
Wong, Willie Wai-Yeung
We study constant mean curvature Lorentzian hypersurfaces of $\mathbb{R}^{1,d+1}$ from the point of view of its Cauchy problem. We completely classify the spherically symmetric solutions, which include among them a manifold isometric to the de Sitter
Externí odkaz:
http://arxiv.org/abs/1404.0223