NEOTROPICAL ALIEN MAMMALS: a data set of occurrence and abundance of alien mammals in the Neotropics.

Biological invasion is one of the main threats to native biodiversity. For a species to become invasive, it must be voluntarily or involuntarily introduced by humans into a nonnative habitat. Mammals were among first taxa to be introduced worldwide for game, meat, and labor, yet the number of species introduced in the Neotropics remains unknown.

A note on stability shifting for the Muskat problem.

In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable and finally return to the unstable regime. We also exhibit numerical evidence of solutions with medium-sized L(∞) norm of the derivative of the initial condition that develop a turning singularity.

Splash singularity for water waves.

We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time.

The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces.

For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible Euler equation, we prove existence locally in time when the Rayleigh-Taylor condition is initially satisfied for a 2D interface. The result for water waves was first obtained by Wu in a slightly different scenario (vanishing at infinity), but our approach is different because it emphasizes the active scalar character of the system and does not require the presence of gravity.

Geological characterization of the Prestige sinking area.

The tanker Prestige sank off NW Iberia on the 19th November 2002. The stern and bow of the Prestige wreck are located on the southwestern edge of the Galicia Bank, at 3565 m and 3830 m water depths, respectively. This bank is a structural high controlled by major faults with predominant N-S, NNE-SSW, and NNW-SEE trends.

Evidence of singularities for a family of contour dynamics equations.

In this work, we show evidence of the existence of singularities developing in finite time for a class of contour dynamics equations depending on a parameter 0 < alpha 0 corresponds to 2D Euler equations, and alpha = 1 corresponds to the surface quasi-geostrophic equation. The singularity is point-like, and it is approached in a self-similar manner.

Almost sharp fronts for the surface quasi-geostrophic equation.

We investigate the evolution of "almost sharp" fronts for the surface quasi-geostrophic equation. This equation was originally introduced in the geophysical context to investigate the formation and evolution of fronts, i.e.

A pointwise estimate for fractionary derivatives with applications to partial differential equations.

This article emphasizes the role played by a remarkable pointwise inequality satisfied by fractionary derivatives in order to obtain maximum principles and Lp-decay of solutions of several interesting partial differential equations. In particular, there are applications to quasigeostrophic flows, in two space variables with critical viscosity, that model the Eckman pumping [see Baroud, Ch. N.

Drops: the collapse of capillary jets.

The appearance of fluid filaments during the evolution of a viscous fluid jet is a commonly observed phenomenon. It is shown here that the break-up of such a jet subject to capillary forces is impossible through the collapse of a uniform filament.