Corpus ID: 219260359

Tightness of radially-symmetric solutions to 2D aggregation-diffusion equations with weak interaction forces

@article{Shu2020TightnessOR,
  title={Tightness of radially-symmetric solutions to 2D aggregation-diffusion equations with weak interaction forces},
  author={Ruiwen Shu},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
  • Ruiwen Shu
  • Published 2020
  • Mathematics
  • arXiv: Analysis of PDEs
  • We prove the tightness of radially-symmetric solutions to 2D aggregation-diffusion equations, where the pairwise attraction force is possibly degenerate at large distance. We first reduce the problem into the finiteness of a time integral in the density on a bounded region, by introducing a new assumption on the interaction potential called the essentially radially contractive (ERC) property. Then we prove this finiteness by using the 2-Wasserstein gradient flow structure, combining with the… CONTINUE READING

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