Exact criterion for global existence and blow up to a degenerate Keller-Segel system

@article{Chen2013ExactCF,
  title={Exact criterion for global existence and blow up to a degenerate Keller-Segel system},
  author={Li Chen and Jinhuan Wang},
  journal={Documenta Mathematica},
  year={2013}
}
A degenerate Keller-Segel system with diffusion exponent m with 2n n+2 < m < 2 − 2 n in multi dimension is studied. An exact criterion for global existence and blow up of solution is obtained. The estimates on L 2n n+2 norm of the solution play important roles in our analysis. These estimates are closely related to the optimal constant in the Hardy- Littlewood- Sobolev inequality. In the case of initial free energy less than a universal constant which depends on the inverse of total mass, there… 
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