Qiuyue Zhang | Searcharxiv

arXiv2025

Strong solutions of fractional Boussinesq equations in an exterior domain

A thermal convection fluid motion in the three-dimensional domain exterior to a sphere is considered. A purely conductive steady state arises due to the fluid heated from the sphere. A fractional equation system is introduced by using spectral presentation. The existence of small strong solutions in a Hilbert space is obtained. The strong solution existence implies the local stability of the steady state, which attracts asymptotically the flows evolving initially from the vector fields close to the steady state.

math.AP↗

arXiv2025

$L^2$ decay estimates of weak solutions to 3D fractional MHD equations in exterior domains

Consider three-dimensional fractional MHD equations in an exterior domain with the Dirichlet boundary condition assumed. Asymptotic behaviours of weak solutions to the three-dimensional exterior fractional MHD equations are studied. $L^2$ decay estimates of the weak solutions are obtained.

math.AP↗

arXiv2022

Fair ranking: a critical review, challenges, and future directions

Ranking, recommendation, and retrieval systems are widely used in online platforms and other societal systems, including e-commerce, media-streaming, admissions, gig platforms, and hiring. In the recent past, a large "fair ranking" research literature has been developed around making these systems fair to the individuals, providers, or content that are being ranked. Most of this literature defines fairness for a single instance of retrieval, or as a simple additive notion for multiple instances of retrievals over time. This work provides a critical overview of this literature, detailing the often context-specific concerns that such an approach misses: the gap between high ranking placements and true provider utility, spillovers and compounding effects over time, induced strategic incentives, and the effect of statistical uncertainty. We then provide a path forward for a more holistic and impact-oriented fair ranking research agenda, including methodological lessons from other fields and the role of the broader stakeholder community in overcoming data bottlenecks and designing effective regulatory environments.

cs.IR↗