96 citations · 400 across the 39 of their papers we have counts for
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Local criteria for blowup in two-dimensional chemotaxis models
Piotr Biler, Tomasz Cieślak, Grzegorz Karch +1
We consider two-dimensional versions of the Keller--Segel model for the chemotaxis with either classical (Brownian) or fractional (anomalous) diffusion. Criteria for blowup of solu…
Optimal criteria for blowup of radial and -symmetric solutions of chemotaxis systems
Piotr Biler, Grzegorz Karch, Jacek Zienkiewicz
A simple proof of concentration of mass equal to for blowing up -symmetric solutions of the Keller--Segel model of chemotaxis in two dimensions with large is given. Mor…
Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane
Piotr Biler, Ignacio Guerra, Grzegorz Karch
As it is well known, the parabolic-elliptic Keller-Segel system of chemotaxis on the plane has global-in-time regular nonnegative solutions with total mass below the critical value…
Time-dependent singularities in the Navier-Stokes system
Grzegorz Karch, Xiaoxin Zheng
We show that, for a given Hölder continuous curve in , there exists a solution to the Navier-Stokes system for an incompressible fluid…