8,915 reputation
12775
bio website williewong.wordpress.com
location
age 31
visits member for 4 years, 11 months
seen 6 hours ago

A mathematician specializing in nonlinear hyperbolic PDEs, geometric analysis of pseudo-Riemannian 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,Xt-h^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 Legendre-Hadamard condition imply a generalized Gårding inequality?
@Denis: for those of us less well-versed, can you indicate which of the works of Lopatinskii is the seminal one you refer to? Thanks in advance.
1d
comment Semi-riemannian 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  riemannian-geometry
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/mathscinet-getitem?mr=279626 and ams.org/mathscinet-getitem?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 sum-of-determinants 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 semi-global 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;DR-inclined, 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?