Ryan Hynd

A Blowup Criterion for Ideal Viscoelastic Flow

We establish an analog of the Beale–Kato–Majda criterion for singularities of smooth solutions of the system of PDE arising in the Oldroyd model for ideal viscoelastic flow.

On Hamilton–Jacobi–Bellman equations with convex gradient constraints

We study PDE of the form

A doubly nonlinear evolution for the optimal Poincare inequality

\max\{F(D^2u,x)-f(x), H(Du)\}=0

Partial Regularity of Weak Solutions of the Viscoelastic Navier--Stokes Equations with Damping

where

Hölder estimates and large time behavior for a nonlocal doubly nonlinear evolution

F

Option Pricing in the Large Risk Aversion, Small Transaction Cost Limit

is uniformly elliptic and convex in its first argument,

Partial Regularity for Type Two Doubly Nonlinear Parabolic Systems

H

The Eigenvalue Problem of Singular Ergodic Control

is convex,

Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control

f

Symmetric surfaces of constant mean curvature in 3

is a given function and