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Research Overview

Chemotaxis in moving fluid

I am interested in the long-time behavior of the Chemotaxis in a dynamic environment.

Flocking and Swarming in Nature

I am interested in various models describing the flocking behavior in nature, the Cucker-Smale and Motsch-Tadmor models included.

Hydrodynamic Stability

I am interested in the mixing and enhanced dissipation effect of shear flows.

https://www.howitworksdaily.com/why-do-birds-flock-together/

Small Scale Creation

I am interested in small scale creation for SQG equations and the Hou-Luo scenario.

Publications

  1. A Note on Enhanced Dissipation of Time-dependent Shear Flows, with Daniel Coble;

  2. Enhanced dissipation and blow-up suppression in a chemotaxis-fluid system​;

  3. Stirring speeds up chemical reaction, with Alexander Kiselev;

  4. Random search in fluid flow aided by chemotaxis, with Yishu Gong,  Alexander Kiselev;

  5. On the Fast Spreading Scenario, with Eitan Tadmor, Andrej Zlatos; 

  6. Enhanced dissipation, hypoellipticity for passive scalar equations with fractional dissipation, Journal of Functional Analysis, 282(3), 2022;

  7. Boundary layer models of the Hou-Luo scenario, with Alexander Kiselev, Journal of Differential Equations, 298, 182--204, 2021;

  8. On the 8π-critical mass threshold of a Patlak-Keller-Segel-Navier-Stokes system, with Yishu Gong, SIAM J. Math. Anal., 53 (3), 2925–2956, 2021;

  9. Inviscid damping and enhanced dissipation of the boundary layer for 2D Navier-Stokes linearized around Couette flow in a channel, with Jacob Bedrossian, Communications in Mathematical Physics, 379(1), 177-226;

  10. A game of alignment: collective behavior of multi-species, with Eitan Tadmor, Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 38 (4), 1031–1053, 2021;

  11. Small scale creation for solutions of the SQG equation, with Alexander Kiselev, Duke Mathematical Journal, 170 (5), 1027–1041, 2021;

  12. Multi-species Patlak-Keller-Segel system, with Eitan Tadmor, Indiana University Mathematics Journal, 70 (4), 1577--1624, 2021;​

  13. Suppression of blow-up in Parabolic-Parabolic Patlak-Keller-Segel via strictly monotone shear flows,  Nonlinearity 31 (2018), no. 8, 3651–3688;

  14.  Suppressing chemotactic blow-up through a fast splitting scenario on the plane, with Eitan Tadmor,  Arch. Ration. Mech. Anal. 232 (2019), no. 2, 951–986;

  15.  Suppression of blow-up in Patlak-Keller-Segel via shear flows, with Jacob Bedrossian,  SIAM J. Math. Anal. 49 (2017), no. 6, 4722–4766; Erratum: Suppression of blow-up in Patlak-Keller-Segel via shear flows, with Jacob Bedrossian, SIAM J. Math. Anal. 50 (2018), no. 6, 6365–6372; 

  16.  Global regularity of two-dimensional flocking hydrodynamics, with Eitan Tadmor, Comptes Rendus Mathematique, Volume 355, Issue 7, July 2017, Pages 795-805;

  17. Distance comparison principle and Grayson type theorem in the three-dimensional curve shortening flow, (2012), arXiv:1209.5146.

Undergraduate Research

  1. Hitting Time of Brownian Motion Subject to Shear Flow, with Despina Chouliara, Yishu Gong, Alexander Kiselev, James Lim, Omar Melikechi, Keenan Powers, Submitted.

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