Research

I am interested in the analysis of PDE's, especially those arising from fluid dynamics and collective behavior.

Here is my Research Statement (updated October 2022).

Publications and Preprints

(Versions posted here may differ slightly from ArXiv or published versions)


11. T.M. Leslie and C. Tan. "Cluster Formation for Weak Solutions of the 1D Euler-alignment System.'' (In preparation)


10. T.M. Leslie and C. Tan. "Sticky Particle Cucker–Smale Dynamics and the Entropic Selection Principle for the 1D Euler-alignment System." arXiv:2108.07715 (Under revision at Communications in PDE's).

9. H. Bahouri, T.M. Leslie, and G. Perelman. "Hs Bounds for the Derivative Nonlinear Schrödinger Equation." arXiv:2107.12297 (accepted for publication in Mathematical Research Letters).

8. D. Lear, T.M. Leslie, R. Shvydkoy, and E. Tadmor. "Geometric Structure of Mass Concentration Sets for Pressureless Euler Alignment Systems.'' Adv. Math. 401 (2022), 108290, 1–30.

7. T.M. Leslie "On the Lagrangian Trajectories for the One-Dimensional Euler Alignment Model without Vacuum Velocity." Comptes Rendus Mathématique 348 (2020), no. 4, 421–433.

6. T.M. Leslie and R. Shvydkoy. "On the Structure of Limiting Flocks in Hydrodynamic Euler Alignment Models." Math. Methods Appl. Sci. 29 (2019), no. 13, 2419–2431.

5. T.M. Leslie. "Weak and Strong Solutions to the Forced Fractional Euler Alignment System." Nonlinearity 32 (2019), no. 1, 46–87.

4. T.M. Leslie and R. Shvydkoy. "The Energy Measure for the Euler and Navier-Stokes Equations." Arch. Ration. Mech. Anal. 230 (2018), no. 2, 459–492.

3. T.M. Leslie and R. Shvydkoy. "Conditions Implying Energy Equality for Weak Solutions of the Navier-Stokes Equations." SIAM J. Math. Anal. 50 (2018), no. 1, 870–890.

2. T.M. Leslie and R. Shvydkoy. "The Energy Balance Relation for Weak Solutions of the Density-Dependent Navier-Stokes Equations." J. Differential Equations 261 (2016), no. 6, 3719–3733.

1. T.M. Leslie, E. Weisman, R. Khatiwada, and J.C. Long. "Prospects for Electron Spin-Dependent Short-Range Force Experiments with Rare Earth Iron Garnet Test Masses.'' Phys. Rev. D 89 (2014), 114022.