# 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} }

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

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 30 REFERENCES

## Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## A Nonlocal Continuum Model for Biological Aggregation

VIEW 1 EXCERPT

## A non-local model for a swarm

VIEW 1 EXCERPT