Very weak solutions and large uniqueness classes of stationary Navier–Stokes equations in bounded domains of R2

AbstractExtending the notion of very weak solutions, developed recently in the three-dimensional case, to bounded domains Ω⊂R2 we obtain a new class of unique solutions u in Lq(Ω), q>2, to the stationary Navier–Stokes system −Δu+u⋅∇u+∇p=f, divu=k, u|∂Ω=g with data f,k,g of low regularity. As a main consequence we obtain a new uniqueness class also for classical weak or strong solutions. Indeed, such a solution is unique if its Lq-norm is sufficiently small or the data satisfy the uniqueness condition of a very weak solution

On the Navier-Stokes equations with rotating effect and prescribed outflow velocity

We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\mathbb{R}^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the prescribed velocity vector is assumed to be parallel to the axis of rotation, in this paper we are interested in a general outflow velocity. In order to use $L^p$-techniques we introduce a new coordinate system, in which we obtain a non-autonomous partial differential equation with an unbounded drift term. We prove that the linearized problem in $\mathbb{R}^d$ is solved by an evolution system on $L^p_{\sigma}(\mathbb{R}^d)$ for $1<p<\infty$. For this we use results about time-dependent Ornstein-Uhlenbeck operators. Finally, we prove, for $p\geq d$ and initial data $u_0\in L^p_{\sigma}(\mathbb{R}^d)$, the existence of a unique mild solution to the full Navier-Stokes system.Comment: 18 pages, to appear in J. Math. Fluid Mech. (published online first

INTEGRANTES EQUIPO DE EDUCACIÓN VIAL EN MADRID [Material gráfico]

Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte. Subdirección General de Coordinación Bibliotecaria, 201

Seasonal variation in impact of non‐native species on tropical seed dispersal networks

This is the final version. Available on open access from Wiley via the DOI in this recordData availability statement: Data available at the Dryad Digital Repository https://doi.org/10.5061/dryad.wm37pvmqw (Costa, Heleno, Dufrene, Huckle, Gabriel, Harrison, et al., 2022).Invasive non-native species can alter animal-mediated seed dispersal interactions and ultimately affect the stability of recipient communities. The degree of such disturbances, however, is highly variable and depends on several factors, two of which have received little attention: the relative timing of native and non-native fruiting phenologies, and the associated variation in relative resource availability across the fruiting period. Both are likely to alter plant–seed disperser interactions threatened by biological invasions. Here we investigated the impact of plant invasions on the seasonal dynamics of frugivory and seed dispersal networks across a large-scale experimental setup and a plant invasion gradient on a tropical island. We recorded fruit and frugivore abundances, and plant–frugivore interactions across eight inselbergs (i.e. rocky outcrops) with different levels of plant invasion during 10 months on the island of Mahé, Seychelles. By combining four sampling methods of plant–frugivore interactions we constructed quantitative seed dispersal networks at all sites across two 5-month seasons: the on-peak and off-peak fruiting season. Our findings showed that, by fruiting mostly synchronously with natives, non-native plants compete with natives for dispersal services, predominantly carried out by native frugivores. Variation in native seed dispersal was driven by plant invasion and seasonality. Specifically, native seed dispersal declined with the degree of invasion; dispersal frequency increased with fruit abundance more strongly during the off-peak fruiting season; and networks became increasingly specialised during off-peak. These results indicated that during the main fruiting peak seed dispersal services were saturated, which likely intensified the competition between native and non-native fruits. When resources were scarce during off-peak fruiting season, native and non-native frugivores were more selective in their fruit choice at sites dominated by non-native plants. We showed that native plant and frugivore populations and native seed dispersal interactions were more vulnerable in invaded plant communities, where non-native plants compete with natives for dispersal services potentially reducing native recruitment. As invasive non-native plants dominate many ecosystems world-wide, particularly on islands, our findings showed that controlling plant invasions in vulnerable native communities can be critical to maintain native ecosystem functions and biodiversity.German Research Foundation (DFG)Portuguese Foundation for Science and Technolog

Quantifying the Detrimental Impacts of Land-Use and Management Change on European Forest Bird Populations

The ecological impacts of changing forest management practices in Europe are poorly understood despite European forests being highly managed. Furthermore, the effects of potential drivers of forest biodiversity decline are rarely considered in concert, thus limiting effective conservation or sustainable forest management. We present a trait-based framework that we use to assess the detrimental impact of multiple land-use and management changes in forests on bird populations across Europe. Major changes to forest habitats occurring in recent decades, and their impact on resource availability for birds were identified. Risk associated with these changes for 52 species of forest birds, defined as the proportion of each species' key resources detrimentally affected through changes in abundance and/or availability, was quantified and compared to their pan-European population growth rates between 1980 and 2009. Relationships between risk and population growth were found to be significantly negative, indicating that resource loss in European forests is an important driver of decline for both resident and migrant birds. Our results demonstrate that coarse quantification of resource use and ecological change can be valuable in understanding causes of biodiversity decline, and thus in informing conservation strategy and policy. Such an approach has good potential to be extended for predictive use in assessing the impact of possible future changes to forest management and to develop more precise indicators of forest health

On the vanishing electron-mass limit in plasma hydrodynamics in unbounded media

We consider the zero-electron-mass limit for the Navier-Stokes-Poisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier-Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier-Stokes system

Understanding continent-wide variation in vulture ranging behavior to assess feasibility of Vulture Safe Zones in Africa: Challenges and possibilities

Protected areas are intended as tools in reducing threats to wildlife and preserving habitat for their long-term population persistence. Studies on ranging behavior provide insight into the utility of protected areas. Vultures are one of the fastest declining groups of birds globally and are popular subjects for telemetry studies, but continent-wide studies are lacking. To address how vultures use space and identify the areas and location of possible vulture safe zones, we assess home range size and their overlap with protected areas by species, age, breeding status, season, and region using a large continent-wide telemetry datasets that includes 163 individuals of three species of threatened Gyps vulture. Immature vultures of all three species had larger home ranges and used a greater area outside of protected areas than breeding and non-breeding adults. Cape vultures had the smallest home range sizes and the lowest level of overlap with protected areas. Rüppell\u27s vultures had larger home range sizes in the wet season, when poisoning may increase due to human-carnivore conflict. Overall, our study suggests challenges for the creation of Vulture Safe Zones to protect African vultures. At a minimum, areas of 24,000 km2 would be needed to protect the entire range of an adult African White-backed vulture and areas of more than 75,000 km2 for wider-ranging Rüppell\u27s vultures. Vulture Safe Zones in Africa would generally need to be larger than existing protected areas, which would require widespread conservation activities outside of protected areas to be successful

Biodiversity post-2020: Closing the gap between global targets and national-level implementation

National and local governments need to step up efforts to effectively implement the post-2020 global biodiversity framework of the Convention on Biological Diversity to halt and reverse worsening biodiversity trends. Drawing on recent advances in interdisciplinary biodiversity science, we propose a framework for improved implementation by national and subnational governments. First, the identification of actions and the promotion of ownership across stakeholders need to recognize the multiple values of biodiversity and account for remote responsibility. Second, cross-sectorial implementation and mainstreaming should adopt scalable and multifunctional ecosystem restoration approaches and target positive futures for nature and people. Third, assessment of progress and adaptive management can be informed by novel biodiversity monitoring and modeling approaches handling the multidimensionality of biodiversity change