I am interested in the analysis of PDE's, especially those arising from fluid dynamics and collective behavior.
I am grateful for the support of the NSF. (DMS-2408585, "Analysis of Continuum PDE's in Collective Behavior and Related Models," awarded August 2024.)
(Versions posted here may differ slightly from ArXiv or published versions)
12. J. Jang and T.M. Leslie. "Separable Motions for Self-Gravitating Hyperelastic Matter." To appear in Communications in Analysis and Mechanics. Also posted as arXiv:2506.02278. 16 pages.
11. T.M. Leslie and C. Tan. "Finite- and Infinite-Time Cluster Formation for Alignment Dynamics on the Real Line." Journal of Evolution Equations 24, no. 8 (2024). 45 pages.
10. T.M. Leslie and C. Tan. "Sticky Particle Cucker–Smale Dynamics and the Entropic Selection Principle for the 1D Euler-alignment System." Communications in Partial Differential Equations, 48 (2023), no. 5, 753-791. (DOI: 10.1080/03605302.2023.2202720.)
9. H. Bahouri, T.M. Leslie, and G. Perelman. "Hs Bounds for the Derivative Nonlinear Schrödinger Equation." Math. Res. Lett. 30 (2023), no. 5, 1299–1333.
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.