Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption

For all suitably regular and radially symmetric initial data (u0,v0) satisfying u0≥0 and v0>0, the present paper establishes the existence of a globally defined pair (u,v) of radially symmetric functions which are continuous in (Ω¯∖{0})×[0,∞) and smooth in (Ω¯∖{0})×(0,∞), and which solve the corresponding initial-boundary value problem for (⋆) with (u(⋅,0),v(⋅,0))=(u0,v0) in an appropriate generalized sense. To the best of our knowledge, this in particular provides the first result on global existence for the three-dimensional version of (⋆) involving arbitrarily large initial data.