| Abstract: |
| We investigate dynamics, stationary states and singular limits for aggregation diffusion models with nonlinear Riesz potentials. Radial stationary states of the dynamics are related with extremals of suitable Hardy-Littlewood-Sobolev inequalities. In the case that aggregation does not dominate over diffusion, radial stationary states also relate to global minimizers of the natural free energy functional. The evolution can be seen as the gradient flow of the free energy, and its analysis requires suitable gradient estimates for the nonlinear Riesz potential. |
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