My work is centered on questions of stability and asymptotic behavior in evolutions equations of fluid dynamics and kinetic theory.

In the realm of fluid dynamics, two concepts are at the core of my investigations:

- Dispersion: In the geophysical context, anisotropic forces due to e.g. gravity or rotation give rise to dispersive effects. These can play an important role in stabilizing a flow (see [2,3,4,5,12] below).
- Mixing: This cascading mechanism is often encountered in question of hydrodynamic stability, and responsible for effects like inviscid damping, enhanced dissipation and meta-stable behavior (see [7,9,11] below).

In kinetic theory, my work focuses on the stability of equilibria in the Vlasov-Poisson equations (see [8,10,13] below).

The following are also available on my arXiv.org page.

- Scattering map for the Vlasov-Poisson system [arXiv:2101.01390]

-- with Patrick Flynn, Zhimeng Ouyang, Benoit Pausader

arXiv preprint 2021,*submitted* - On the stabilizing effect of rotation in the 3d Euler equations [arXiv:2010.10460]

-- with Yan Guo, Chunyan Huang, Benoit Pausader

arXiv preprint 2020,*submitted* - Mixing and diffusion for rough shear flows [arXiv:2009.12268]

-- with Maria Colombo, Michele Coti Zelati

arXiv preprint 2020,*submitted* - Stability of a point charge for the Vlasov-Poisson system: the radial
case [arXiv:2008.08013]

-- with Benoit Pausader

arXiv preprint 2020, to appear in*Communications in Mathematical Physics* - Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations [arXiv:2007.11547]

-- with Michele Coti Zelati, Tarek M. Elgindi

arXiv preprint 2020,*submitted* - On the asymptotic behavior of solutions to the Vlasov-Poisson system [arXiv:2005.03617]

-- with Alexandru D. Ionescu, Benoit Pausader, Xuecheng Wang

arXiv preprint 2020,*submitted* - Enhanced dissipation in the Navier-Stokes equations near the Poiseuille flow [arXiv:1901.01571]

-- with Michele Coti Zelati, Tarek M. Elgindi

*Communications in Mathematical Physics 378, 987–1010 (2020)* - The Surface Quasi-Geostrophic Equation with Random Diffusion [arXiv:1806.03734]

-- with Tristan Buckmaster, Andrea Nahmod, Gigliola Staffilani

*International Mathematics Research Notices, Volume 2020, Issue 23, November 2020, Pages 9370–9385* - On the Global Stability of a Beta-Plane Equation [arXiv:1610.03479]

-- with Fabio Pusateri

*Analysis & PDE, Vol. 11 (2018), No. 7, 1587-1624* - Convergence to Stratified Flow for an Inviscid 3D Boussinesq System [arXiv:1509.09216]

*Commun. Math. Sci. Vol. 16, No. 6, pp. 1713-1728* - Long Time Stability for Solutions of a Beta-Plane Equation [arXiv:1509.05355]

-- with Tarek M. Elgindi

*Comm. Pure Appl. Math., Volume 70, Issue 8, August 2017, Pages 1425-1471* - Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems [arXiv:1410.1415]

-- with Tarek M. Elgindi

*SIAM Journal on Mathematical Analysis, 47 (6), Pages 4672-4684* - Non-uniqueness of Weak Solutions to the Wave Map Problem [arXiv:1310.4419]

*Ann. Inst. H. Poincaré (C) Analyse Non Linéaire, Volume 32, Issue 3, May-June 2015, Pages 519-532*