We prove the global well-posedness of the two-dimensional Boussinesq equations with only vertical dissipation. The initial data (Formula presented.) are required to be only in the space (Formula presented.) , and thus our result generalizes that of Cao and Wu (Arch Rational Mech Anal, 208:985–1004, 2013), where the initial data are assumed to be in (Formula presented.). The assumption on the initial data is at the minimal level that is required to guarantee the uniqueness of the solutions. A logarithmic type limiting Sobolev embedding inequality for the (Formula presented.) norm, in terms of anisotropic Sobolev norms, and a logarithmic type Gronwall inequality are established to obtain the global in time a priori estimates, which guarantee the local solution to be a global one.

We establish some conditional uniqueness of weak solutions to the viscous primitive equations, and as an application, we prove the global existence and uniqueness of weak solutions, with the initial data taken as small L∞ perturbations of functions in the space X = {v ∈ (L6(Ω))2|∂z v ∈ (L2(Ω))2}; in particular, the initial data are allowed to be discontinuous. Our result generalizes in a uniform way the result on the uniqueness of weak solutions with continuous initial data and that of the so-called z-weak solutions.

In this paper, we consider a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture, which was derived in Frierson et al (2004 Commum. Math. Sci. 2 591-626). We establish the global existence and uniqueness of strong solutions to this system, with initial data in H1, for each fixed convective adjustment relaxation time parameter ϵ > 1. Moreover, if the initial data possess slightly more regularity than H 1, then the unique strong solution depends continuously on the initial data. Furthermore, by establishing several appropriate ϵ-independent estimates, we prove that the system converges to a limiting system as the relaxation time parameter ϵ tends to zero, with a convergence rate of the order O(√ϵ). Moreover, the limiting system has a unique global strong solution for any initial data in H1 and such a unique strong solution depends continuously on the initial data if the initial data posses slightly more regularity than H1. Notably, this solves the viscous version of an open problem proposed in the above mentioned paper of Frierson, Majda and Pauluis.

In this paper, we consider the Cauchy problem to the tropical climate model derived by Frierson-Majda-Pauluis in [15], which is a coupled system of the barotropic and baroclinic modes of the velocity and the typical midtropospheric temperature. The system considered in this paper has viscosities in the momentum equations, but no diffusivity in the temperature equation. We establish here the global well-posedness of strong solutions to this model. In proving the global existence of strong solutions, to overcome the difficulty caused by the absence of the diffusivity in the temperature equation, we introduce a new velocity w (called the pseudo baroclinic velocity), which has more regularities than the original baroclinic mode of the velocity. An auxiliary function φ, which looks like the effective viscous flux for the compressible Navier-Stokes equations, is also introduced to obtain the L∞ bound of the temperature. Regarding the uniqueness, we use the idea of performing suitable energy estimates at level one order lower than the natural basic energy estimates for the system.

Among metals used for CO2electroreduction in water, Cu appears to be unique in its ability to produce C2+ products like ethylene. Bimetallic combinations of Cu with other metals have been investigated with the goal of steering selectivityviacreating a tandem pathway through the CO intermediate or by changing the surface electronic structure. Here, we demonstrate a facile cation exchange method to synthesize Ag/Cu electrocatalysts for CO2reduction using Cu sulfides as a growth template. Beginning with Cu2−xS nanosheets (C-nano-0, 100 nm lateral dimension, 14 nm thick), varying the Ag+concentration in the exchange solution produces a gradual change in crystal structure from Cu7S4to Ag2S, as the Ag/Cu mass ratio varies from 0.3 to 25 (CA-nano-x,xindicating increasing Ag fraction). After cation exchange, the nanosheet morphology remains but with increased shape distortion as the Ag fraction is increased. Interestingly, the control (C-nano-0) and cation exchanged nanosheets have very high faradaic efficiency for producing formate at low overpotential (−0.2 Vvs.RHE). The primary effect of Ag incorporation is increased production of C2+ products at −1.0 Vvs.RHE compared with C-nano-0, which primarily produces formate. Cation exchange can also be used to modify the surface of Cu foils. A two-step electro-oxidation/sulfurization process was used to form Cu sulfides on Cu foil (C-foil-x) to a depth of a few 10 s of microns. With lower Ag+concentrations, cation exchange produces uniformly dispersed Ag; however, at higher concentrations, Ag particles nucleate on the surface. During CO2electroreduction testing, the product distribution for Ag/Cu sulfides on Cu foil (CA-foil-x-y) changes in time with an initial increase in ethylene and methane production followed by a decrease as more H2is produced. The catalysts undergo a morphology evolution towards a nest-like structure which could be responsible for the change in selectivity. For cation-exchanged nanosheets (CA-nano-x), pre-reduction at negative potentials increases the CO2reduction selectivity compared to tests of as-synthesized material, although this led to the aggregation of nanosheets into filaments. Both types of bimetallic catalysts are capable of selective reduction of CO2to multi-carbon products, although the optimal configurations appear to be metastable.

In this study, a regional climate model (RCM) is employed to investigate the effect of irrigation on hydrology over California through implementing a “realistic irrigation” scheme. Our results indicate that the RCM with a realistic irrigation scheme commonly practiced in California can capture the soil moisture and evapotranspiration (ET) variation very well in comparison with the available in situ and remote sensing data. The RCM results show significant improvement in comparison with those outputs from the default run and the commonly used runs with fixed soil moisture at field capacity. Furthermore, the model reproduces the observed decreasing trends of the reference ET (i.e., ET0) from the California Irrigation Management Information System (CIMIS). The observed decreasing trend is most likely due to the decreasing trend of downward solar radiation shown by models and CIMIS observations. This issue is fundamental in projecting future irrigation water demand. The deep soil percolation rate changes depending on the irrigation method and irrigation duration. Finally, the model results show that precipitation change due to irrigation in California is relatively small in amount and mainly occurs along the midlatitudes in the western United States.

In this paper, we study the following problem. Given a database and a set of queries, we want to find a set of views that can compute the answers to the queries, such that the amount of space, in bytes, required to store the viewset is minimum on the given database. (We also handle problem instances where the input has a set of database instances, as described by an oracle that returns the sizes of view relations for given view definitions.) This problem is important for applications such as distributed databases, data warehousing, and data integration. We explore the decidability and complexity of the problem for workloads of conjunctive queries. We show that results differ significantly depending on whether the workload queries have self-joins. Further, for queries without self-joins we describe a very compact search space of views, which contains all views in at least one optimal viewset. We present techniques for finding a minimum-size viewset for a single query without self-joins by using the shape of the query and its constraints, and validate the approach by extensive experiments.