Search Results (2)

This paper deals with an initial-boundary value problem modeling the unidirectional pressure-driven flow of a second grade fluid in a plane channel with impermeable solid walls. On the channel walls, Navier-type slip boundary conditions are stated. Our aim is to investigate the well-posedness of this problem and obtain its analytical solution under weak regularity requirements on a function describing the velocity distribution at initial time. In order to overcome difficulties related to finding classical solutions, we propose the concept of a generalized solution that is defined as the limit of a uniformly convergent sequence of classical solutions with vanishing perturbations in the initial data. We prove the unique solvability of the problem under consideration in the class of generalized solutions. The main ingredients of our proof are a generalized Abel criterion for uniform convergence of function series and the use of an orthonormal basis consisting of eigenfunctions of the related Sturm–Liouville problem. As a result, explicit expressions for the flow velocity and the pressure in the channel are established. The constructed analytical solutions favor a better understanding of the qualitative features of time-dependent flows of polymer fluids and can be applied to the verification of relevant numerical, asymptotic, and approximate analytical methods. Full article

We present the results from a search for high-redshift radio galaxy (HzRG) candidates using 1.28 GHz data in the Abell 2751 field drawn from the MeerKAT Galaxy Cluster Legacy Survey (MGCLS). We used the HzRG criteria that a radio source is undetected in all-sky optical and infrared catalogues and that it has a very steep radio spectrum. We used the likelihood ratio method for cross-matching the radio catalogue against multi-wavelength galaxy catalogues from the Dark Energy Camera Legacy Survey (DECaLS) and the All-sky Wide Infrared Survey Explorer (AllWISE). For those radio sources with no multi-wavelength counterpart, we further implemented a radio spectral index criterium of $\alpha <-1$, using in-band spectral index measurements from the wide-band MeerKAT data. Using a 5$\sigma$ signal-to-noise cut on the radio flux densities, we found a total of 274 HzRG candidates: 179 ultra-steep spectrum sources and 95 potential candidates, which could not be ruled out as they had no spectral information available. The spectral index assignments in this work were complete above a flux density of 0.3 mJy, which is at least an order of magnitude lower than existing studies in this frequency range or when extrapolating from lower frequency limits. Our faintest HzRG candidates with and without an in-band spectral index measurement had a 1.28 GHz flux density of 57 ± 8 $\mathsf{\mu }$Jy and 68 ± 13 $\mathsf{\mu }$Jy, respectively. Although our study is not complete down to these flux densities, our results indicate that the sensitivity and bandwidth of the MGCLS data make them a powerful radio resource to search for HzRG candidates in the Southern sky, with 20 of the MGCLS pointings having similar image quality as the Abell 2751 field and full coverage in both DECaLS and AllWISE. Data at additional radio frequencies will be needed for the faintest source populations, which could be provided in the near future by the MeerKAT UHF band (580–1015 MHz) at a similar resolution (∼8–10″). Full article