Global existence for the kinetic chemotaxis model without pointwise   memory effects, and including internal variables
  This paper is concerned with the kinetic model of Othmer-Dunbar-Alt for bacterial motion. Following a previous work, we apply the dispersion and Strichartz estimates to prove global existence under several borderline growth assumptions on the turning kernel. In particular we study the kinetic model with internal variables taking into account the complex molecular network inside the cell. 
Nikolaos Bournaveas, Vincent Calvez (DMA)