63 citations · 279 across the 24 of their papers we have counts for
15 papers · 1 filter
Zeroes of Eigenfunctions of Schrödinger Operators after Schwartzman
Willie Wai-Yeung Wong
Consider a complete, connected, smooth, oriented Riemannian manifold with boundary, such that the first Betti number vanishes. Sol Schwartzman proved that for Schrödinger o…
Geometric analysis of 1+1 dimensional quasilinear wave equations
Leonardo Enrique Abbrescia, Willie Wai Yeung Wong
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-necessari…
Dispersive estimates for Klein-Gordon equations via a physical space approach
Willie Wai Yeung Wong
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 …
Global versions of Gagliardo-Nirenberg-Sobolev inequality and applications to wave and Klein-Gordon equations
Leonardo Abbrescia, Willie Wai Yeung Wong
We prove global, or space-time weighted, versions of the Gagliardo-Nirenberg interpolation inequality, with () endpoint, adapted to a hyperboloidal foliation. The…
Global nearly-plane-symmetric solutions to the membrane equation
Leonardo Abbrescia, Willie Wai Yeung Wong
We prove that any simple planar travelling wave solution to the membrane equation in spatial dimension with bounded spatial extent is globally nonlinearly stable under s…
Small data global existence and decay for two dimensional wave maps
Willie Wai Yeung Wong
We prove the small-data global existence for the wave-map equation on using a variant of the vector field method. The main innovations lie in the introduction of…
A commuting-vector-field approach to some dispersive estimates
Willie Wai Yeung Wong
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 Schroding…
Singularities of axially symmetric time-like minimal submanifolds in Minkowski space
Willie Wai-Yeung Wong
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…
Global Existence for the Minimal Surface Equation on
Willie Wai Yeung Wong
In a 2004 paper, Lindblad demonstrated that the minimal surface equation on describing graphical time-like minimal surfaces embedded in enjoy…
Stable shock formation for nearly simple outgoing plane symmetric waves
Jared Speck, Gustav Holzegel, Jonathan Luk +1
In an influential 1964 article, P. Lax studied genuinely nonlinear strictly hyperbolic PDE systems (in one spatial dimension). Using the method of Riemann invariants,…
Shock Formation in Small-Data Solutions to Quasilinear Wave Equations
Jared Speck
In his 2007 monograph, D. Christodoulou proved a breakthrough result giving a detailed description of the formation of shocks in solutions to the relativistic Euler equations in th…
Shock Formation in Small-Data Solutions to Quasilinear Wave Equations: An Overview
Gustav Holzegel, Sergiu Klainerman, Jared Speck +1
In his 2007 monograph, D. Christodoulou proved a remarkable result giving a detailed description of shock formation, for small -initial conditions ( sufficiently large), in…
Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space
Roland Donninger, Joachim Krieger, Jeremie Szeftel +1
We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian m…
On type I blow up formation for the critical NLW
Joachim Krieger, Willie Wong
We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on , that is adapted to continuation pas…
On strong unique continuation of coupled Einstein metrics
Willie Wai-Yeung Wong, Pin Yu
The strong unique continuation property for Einstein metrics can be concluded from the well-known fact that Einstein metrics are analytic in geodesic normal coordinates. Here we gi…