Tak Kwong Wong

ON THE LOCAL WELL-POSEDNESS OF THE PRANDTL AND HYDROSTATIC EULER EQUATIONS WITH MULTIPLE MONOTONICITY REGIONS ∗

We find a new class of data for which the Prandtl boundary layer equations and the hydrostatic Euler equations are locally in time well-posed. In the case of the Prandtl equations, if the initial datum

Blowup of solutions of the hydrostatic Euler equations

u_0

Asymptotic harvesting of populations in random environments

is monotone on a number of intervals (on some strictly increasing, on some strictly decreasing) and analytic on the complement of these intervals, we show that the local existence and uniqueness hold. The same result is true for the hydrostatic Euler equations if we assume these conditions for the initial vorticity

Axisymmetric flow of ideal fluid moving in a narrow domain: A study of the axisymmetric hydrostatic Euler equations

\omega_0=\partial_y u_0

Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods

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Long time solutions for a Burgers-Hilbert equation via a modified energy method

In this paper we prove that for a certain class of initial data, smooth solutions of the hydrostatic Euler equations blow up in finite time.

The Inverse First Passage Time Problem for killed Brownian motion

We consider the harvesting of a population in a stochastic environment whose dynamics in the absence of harvesting is described by a one dimensional diffusion. Using ergodic optimal control, we find the optimal harvesting strategy which maximizes the asymptotic yield of harvested individuals. To our knowledge, ergodic optimal control has not been used before to study harvesting strategies. However, it is a natural framework because the optimal harvesting strategy will never be such that the population is harvested to extinction—instead the harvested population converges to a unique invariant probability measure. When the yield function is the identity, we show that the optimal strategy has a bang–bang property: there exists a threshold

Optimal Liquidation Problems in a Randomly-Terminated Horizon

x^*>0