bio  website  williewong.wordpress.com 

location  
age  31  
visits  member for  4 years, 11 months 
seen  6 hours ago  
stats  profile views  8,995 
A mathematician specializing in nonlinear hyperbolic PDEs, geometric analysis of pseudoRiemannian manifolds, and general relativity.
6h

accepted  Commutator of Lie derivative and codifferential? 
6h

answered  Commutator of Lie derivative and codifferential? 
6h

reviewed  Close Fractional Schrödinger equation 
6h

reviewed  Reviewed calculating E(Xt^2,Xth^2) with Xt normal(0,sigma^2) 
9h

comment 
Analogous to a PDE but where independent variable is a function
There's something screwy about your notation that you should fix. As far as I can tell in equation (1) $u$ is independent of $t$; so $\partial_t u$ doesn't make sense. What is $\dot{x}$? Should it be treated as formally just a different variable? In (2), what is $q(u(x))$'s dependence on $t$? What is the meaning of the $\partial_{u(x)}$? If it is a Frechet differential, then you are adding a vector in an infinite dimnsional space to a scalar, and your equation has a type error. 
15h

comment 
Does the LegendreHadamard condition imply a generalized Gårding inequality?
@Denis: for those of us less wellversed, can you indicate which of the works of Lopatinskii is the seminal one you refer to? Thanks in advance. 
1d

comment 
Semiriemannian hypersurfaces
@Ergonvi: it is a linear (hence smooth) function restricted over a compact smooth manifold. Of course it has critical points. 
1d

reviewed  Leave Open Question on the local existence theory for the classical solution for the incompressible fluid dynamics equation 
Jan 13 
awarded  riemanniangeometry 
Jan 12 
revised 
Compact riemannian manifolds with boundary that have infinite volume?
added 551 characters in body 
Jan 12 
answered  Compact riemannian manifolds with boundary that have infinite volume? 
Jan 12 
reviewed  Leave Open Compact riemannian manifolds with boundary that have infinite volume? 
Jan 12 
comment 
Compact riemannian manifolds with boundary that have infinite volume?
Even with the edits I still don't understand what you are looking for: in your example the metric wrt which you have a infinite volume is different from the induced metric wrt which you exhibit the "compactness". I don't think your edits have fully addressed Joonas' or Ryan's questions; namely what exactly is the object that you are looking for? // For example, taking a look at your paper, on page 8 the construction of the scattering disk does not have anything to do with geodesics per se, so maybe you are emphasizing the wrong things in your question statement. 
Jan 8 
comment 
Schrodinger equation with magnetic vector potential
Quite frequently (though I cannot guarantee it) in this context the reference to "Kato's methods" refers to the developments centered around his two papers ams.org/mathscinetgetitem?mr=279626 and ams.org/mathscinetgetitem?mr=326483 The theory is strong enough that oftentimes authors just refers to it as a blackbox guaranteeing the existence of "evolution" for the linear operator. But you can probably find something interesting if you look at MathSciNet references to those two papers. 
Dec 11 
reviewed  Close A sumofdeterminants identity 
Dec 10 
reviewed  Close Finding conditions to guarantee existence of solutions to IVP 
Dec 10 
comment 
Finding conditions to guarantee existence of solutions to IVP
There are two parts to your question: (a) is the local existence, which is essentially addressed by Peano. (b) is the semiglobal existence (solution exists for all $t\geq 0$), this is where conditions on $b(t)$ and $x_0$ seems to be more relevant. Can you please clarify your question? 
Dec 10 
reviewed  Close Solution of a second order nonlinear ode 
Dec 10 
comment 
Can there be ordinals larger than those contained in Ord, and if so, can they be used to extend the constructible universe $L$?
@ThomasBenjamin: I hope you don't mind my editing. For the sake of those TL;DRinclined, I moved your simplified question from the bottom of the post to near the top, where it would be more visible. 
Dec 10 
reviewed  Leave Closed Have there been any new developments in the Firoozbakht conjecture? 