Publications

  1. Small scale formation for the 2D Boussinesq equation, with A. Kiselev and J. Park, preprint.
  2. Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel, with J. Carrillo, D. Gómez-Castro and C. Zeng, to appear in Arch. Ration. Mech. Anal.
  3. Two-species competition model with chemotaxis: well-posedness, stability and dynamics, with G. Li, Nonlinearity,35(3) 1329, 2022.
  4. Small scale formations in the incompressible porous media equation, with A. Kiselev, to appear in Arch. Ration. Mech. Anal.
  5. Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results, with J. Gómez-Serrano, J. Park and J. Shi, Comm. Math. Phys., 386, 1845-1879, 2021.
  6. Remarks on stationary and uniformly-rotating vortex sheets: Flexibility results, with J. Gómez-Serrano, J. Park and J. Shi, Phil. Trans. R. Soc. A., 380, no. 2226, 20210045, 2022.
  7. Sharp stability for the interaction energy, with X. Yan, to appear in Arch. Ration. Mech. Anal.
  8. Chemotaxis and reactions in biology, with A. Kiselev, F. Nazarov and L. Ryzhik, to appear in J. Eur. Math. Soc.
  9. Symmetry of hypersurfaces with ordered mean curvature in one direction, with Y.Y. Li and X. Yan, Calc. Var. PDE, 60, 173, 2021.
  10. Uniqueness and non-uniqueness of steady states of aggregation-diffusion equations, with M. Delgadino and X. Yan, Comm. Pure Appl. Math., 75, 3-59, 2022.
  11. Symmetry in stationary and uniformly-rotating solutions of active scalar equations, with J. Gómez-Serrano, J. Park and J. Shi, Duke Math Journal, 170, 2957-3038, 2021.
  12. Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, with J. Carrillo and K. Craig, Active Particles, Volume 2, 65-108, 2019.
  13. Nonlinear Aggregation-Diffusion Equations: Radial Symmetry and Long Time Asymptotics, with J. Carrillo, S. Hittmeir and B. Volzone, Invent. Math., 218 (3), 889-977, 2019.
  14. Congested aggregation via Newtonian interaction, with K. Craig and I. Kim, Arch. Ration. Mech. Anal., 227(1): 1-67, 2018.
  15. Finite time singularity formation for the modified SQG patch equation, with A. Kiselev, L. Ryzhik and A. Zlatoš, Ann. of Math., 184(3): 909-948, 2016.
  16. Local regularity for the modified SQG patch equation, with A. Kiselev and A. Zlatoš, Comm. Pure Appl. Math., 70(7): 1253-1315, 2017.
  17. On the finite-time blowup of a 1D model for the 3D axisymmetric Euler equations, with K. Choi, T. Hou, A. Kiselev, G. Luo and V. Sverak, Comm. Pure Appl. Math., 70(11): 2218-2243, 2017.
  18. Mixing and un-mixing by incompressible flows, with A. Zlatoš, J. Eur. Math. Soc., 19(7): 1911–1948, 2017.
  19. Global regularity of chemotaxis equations with advection, with S. Khan, J. Johnson, and E. Cartee, Involve 9(1): 119-131, 2016.
  20. Finite time blow up for a 1D model of 2D Boussinesq system, with K. Choi and A. Kiselev, Commun. Math. Phys.,334: 1667-1679, 2015.
  21. Stability and dynamics of magnetocapillary interactions, with R. Chinomona, J. Lajeunesse, W.H. Mitchell, and S.E. Spagnolie, Soft Matter, 11 (9), 1828-1838, 2015.
  22. Quasi-static evolution and congested crowd transport, with D. Alexander and I. Kim, Nonlinearity, 27: 1-36, 2014.
  23. Confinement for repulsive-attractive kernels, with D. Balagué and J. A. Carrillo, Discret. Contin. Dyn. S. Ser. B, 19: 1227-1248, 2014.
  24. Asymptotic behavior for critical Patlak-Keller-Segel model and an repulsive-attractive aggregation equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31(1): 81-101, 2014.
  25. Blow-up dynamics for the aggregation equation with degenerate diffusion, with A. L. Bertozzi, Physica D, special issue on Emergent behaviour in multi-particle systems with non-local interactions, 260: 77-89, 2013.
  26. An aggregation equation with degenerate diffusion: qualitative property of solutions, with L. Chayes and I. Kim, SIAM J. Math. Anal, 45(5):2597-3049, 2013.
  27. The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle, with I. Kim, SIAM J. Math. Anal., 44(2):568-602, 2012.