Global existence and decay for solutions of the Hele-Shaw flow with injection

We study the global existence and decay to spherical equilibrium of Hele-Shaw flows with surface tension. We prove that without injection of fluid, perturbations of the sphere decay to zero exponentially fast. On the other hand, with a time-dependent rate of fluid injection into the Hele-Shaw cell, the distance from the moving boundary to an expanding sphere (with time-dependent radius) also decays to zero but with an algebraic rate, which depends on the injection rate of the fluid.Comment: 25 Page

On the Motion of Vortex Sheets with Surface Tension in the 3D Euler Equations with Vorticity

We prove well-posedness of vortex sheets with surface tension in the 3D incompressible Euler equations with vorticity.Comment: 28 page

Navier-Stokes equations interacting with a nonlinear elastic fluid shell

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic fluid shell. The fluid motion is governed by the Navier-Stokes equations, while the fluid shell is modeled by a bending energy which extremizes the Willmore functional and a membrane energy that extremizes the surface area of the shell. The fluid flow and shell deformation are coupled together by continuity of displacements and tractions (stresses) along the moving material interface. We prove existence and uniqueness of solutions in Sobolev spaces.Comment: 56 pages, 1 figur

Estimating features of a distribution from binomial data

A statistical problem that arises in several fields is that of estimating the features of an unknown distribution, which may be conditioned on covariates, using a sample of binomial observations on whether draws from this distribution exceed threshold levels set by experimental design. One application is destructive duration analysis, where the process is censored at an observation test time. Another is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values placed by consumers on a public good such as endangered species. Sample consumers are asked whether they would vote for a referendum that would provide the good at a cost speci…ed by experimental design. This paper provides estimators for moments and quantiles of the unknown distribution in this problem.

Ethical Issues Arising When a Lawyer Leaves a Firm: Restrictions on Practice

Restriction on covenants not to compete have been a long-time feature of legal practice. Rules prohibiting law firms from restricting lawyers\u27 ability to practice or imposing penalties on lawyers that leave a firm attempt to balance the law firm\u27s interest in survival in a competitive market with the countervailing interests of attorney mobility, and protecting clients\u27 choice of counsel. Restrictions on covenants not to compete should be vigorously enforced, and the exception that allows for the forfeiture of retirement benefits by attorneys that choose to leave a firm should be narrowly applied to only those funds to which the departing attorney is not already entitled

Ethical Issues Arising When a Lawyer Leaves a Firm: Restrictions on Practice

Restriction on covenants not to compete have been a long-time feature of legal practice. Rules prohibiting law firms from restricting lawyers\u27 ability to practice or imposing penalties on lawyers that leave a firm attempt to balance the law firm\u27s interest in survival in a competitive market with the countervailing interests of attorney mobility, and protecting clients\u27 choice of counsel. Restrictions on covenants not to compete should be vigorously enforced, and the exception that allows for the forfeiture of retirement benefits by attorneys that choose to leave a firm should be narrowly applied to only those funds to which the departing attorney is not already entitled

What Statutes Mean: Interpretive Lessons from Positive Theories of Communication and Legislation

How should judges interpret statutes? For some scholars and judges, interpreting statutes requires little more than a close examination of statutory language, with perhaps a dictionary and a few interpretive canons nearby. For others, statutory interpretation must be based upon an assessment of a statute\u27s underlying purpose, an evaluation of society\u27s current norms and values, or a normative objective, such as the law\u27s integrity. With such differences squarely framed in the literature, it is reasonable to ask whether anything of value can be added. We contend that there is

OPTIMAL SPATIAL ALLOCATION OF WASTE MANAGEMENT PRACTICES TO REDUCE PHOSPHORUS POLLUTION IN A WATERSHED

Phosphorus pollution from excessive litter application and municipal discharges causes eutorphication of lakes in the Eucha-Spavinaw watershed in eastern Oklahoma and western Arkansas. Consequent algae blooms impair the taste of drinking water supply drawn from the watershed and reduce the recreational values of the lakes. The paper shows how GIS data based biophysical modeling can be used to derive spatially optimal, least-cost allocation of agricultural management practices to be combined with optimal wastewater treatment activity from the point source in order to achieve socially optimal phosphorus load in the watershed. The optimal level of phosphorus load is determined by equating marginal abatement with marginal damage cost. Transportation activities in the model allow for transportation of litter within and out of the watershed. Results show uniform regulation of litter application is excessively costly relative to measures that encourage adoption of management practices that equate marginal abatement costs across pollution sources. The results also show that change in the land use patterns in a long-run and using alum based litter additives in short-run are economically efficient management options.Environmental Economics and Policy,