On the self-similar stability of the parabolic-parabolic Keller-Segel equation

Frank Alvarez Borges, Kleber Carrapatoso, Stéphane Mischler

We consider the parabolic-parabolic Keller-Segel equation in the plane and prove the nonlinear exponential stability of the self-similar profile in a quasi parabolic-elliptic regim…