4 papers · 1 filter
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…
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…
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.…