The 8π -problem for radially symmetric solutions of a chemotaxis model in the plane Piotr BILER 1 , Grzegorz KARCH 1 , Philippe LAURENC ¸ OT 2 , Tadeusz NADZIEJA 3 1 Instytut Matematyczny, Uniwersytet Wroclawski, pl. Grunwaldzki 2/4, 50–384 Wroclaw, Poland {Piotr.Biler,Grzegorz.Karch}@math.uni.wroc.pl 2 Math´ ematiques pour l’Industrie et la Physique, CNRS UMR 5640, Universit´ e Paul Sabatier – Toulouse 3, 118 route de Narbonne, F–31062 Toulouse Cedex 4, France laurenco@mip.ups-tlse.fr 3 Wydzia l Matematyki, Informatyki i Ekonometrii, UniwersytetZielonog´orski, ul. Szafrana 4a, 65–516 Zielona G´ora, Poland T.Nadzieja@wmie.uz.zgora.pl February 28, 2006 Abstract The existence, uniqueness and large time behaviour of radially sym- metric solutions to a chemotaxis system in the plane R 2 are studied either for the critical value of the mass equal to 8π or in the subcritical case. Key words and phrases: chemotaxis system, infinite domain, radially symmetric solutions, critical mass. 2000 Mathematics Subject Classification: 35Q, 35K60, 35B40. 1