511 citations · 1.7k across the 69 of their papers we have counts for
5 papers · 1 filter
On nonexistence of splash singularities for the -SQG patches
Alexander Kiselev, Xiaoyutao Luo
In this paper, we consider patch solutions to the -SQG equation and derive new criteria for the absence of splash singularity where different patches or parts of the same patch…
Stirring Speeds Up Chemical Reaction
Siming He, Alexander Kiselev
We consider absorbing chemical reactions in a fluid flow modeled by the coupled advection-reaction-diffusion equations. In these systems, the interplay between chemical diffusion a…
Random search in fluid flow aided by chemotaxis
Yishu Gong, Siming He, Alexander Kiselev
In this paper, we consider the dynamics of a 2D target-searching agent performing Brownian motion under the influence of fluid shear flow and chemical attraction. The analysis is m…
Chemotactic Reaction Enhancement in One Dimension
Yishu Gong, Alexander Kiselev
Chemotaxis, the directional locomotion of cells towards a source of a chemical gradient, is an integral part of many biological processes - for example, bacteria motion, single-cel…
Small scale formations in the incompressible porous media equation
Alexander Kiselev, Yao Yao
We construct examples of solutions to the incompressible porous media (IPM) equation that must exhibit infinite in time growth of derivatives provided they remain smooth. As an app…