11 citations · 16 across the 5 of their papers we have counts for
6 papers
A Nash stratification inequality and global regularity for a chemotaxis-fluid system on general 2D domains
Alexander Kiselev, Naji A. Sarsam
Incompressible fluid advection has been shown to facilitate singularity suppression in various differential equations, often by mixing-enhanced diffusion or by dimension-reduction…
Reaction enhancement by flux-limited chemotaxis
Jing An, Alexander Kiselev, Yao Yao
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions; one example is the immune syste…
Chemotaxis and Reactions in Anomalous Diffusion Dynamics
Crystianne L. De Andrade, Alexander A. Kiselev
Chemotaxis and reactions are fundamental processes in biology, often intricately intertwined. Chemotaxis, in particular, can be crucial in maintaining and accelerating a reaction.…
Finite time blow-up in a 1D model of the incompressible porous media equation
Alexander Kiselev, Naji A. Sarsam
We derive a PDE that models the behavior of a boundary layer solution to the incompressible porous media (IPM) equation posed on the 2D periodic half-plane. This 1D IPM model is a…
Suppression of Chemotactic Blowup by Strong Buoyancy in Stokes-Boussinesq Flow with Cold Boundary
Zhongtian Hu, Alexander Kiselev
In this paper, we show that the Keller-Segel equation equipped with zero Dirichlet Boundary condition and actively coupled to a Stokes-Boussinesq flow is globally well-posed provid…
Diffusion and Mixing in Fluid Flow
P. Constantin, A. Kiselev, L. Ryzhik +1
We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the…