Singularities of Solutions to Chemotaxis Systems (De Gruyter Series in Mathematics and Life Sciences 6) (2019. XXIV, 207 S. 3 b/w ill. 240 mm)

The Keller-Segel model for chemotaxis is a prototype of nonlocal systems describing concentration phenomena in physics and biology. While the two-dimensional theory is by now quite complete, the questions of global-in-time solvability and blowup characterization are largely open in higher dimensions. In this book, global-in-time solutions are constructed under (nearly) optimal assumptions on initial data and rigorous blowup criteria are derived.