I am currently a research scientist at New-York University Abu Dhabi. My research interests are mainly the study of PDEs, in particular, those arising in fluid mechanics. I mainly use tools from Harmonic /Functional Analysis.
email: omar..lazar (at) nyu.edu
Communication in Mathematical Physics, 322, no. 1, pp. 73-93 (2013).
Journal of Mathematical Fluid Mechanics, 17-3, pp. 533-549 (2015)
Infinite energy solutions for a 1D transport equation with nonlocal velocity (with Pierre-Gilles Lemarié-Rieusset).
Dynamics of PDEs Vol. 13, No. 2, pp. 107-131 (2016)
Journal of Differential Equations, Volume 261, Issue 9, pp 4974-4996 (2016).
Global existence of weak solutions to dissipative transport equations with nonlocal velocity (with Hantaek Bae and Rafael Granero-Belinchon).
Nonlinearity, Vol. 31, No. 4 (2018), pp. 1484-1515.
On the local and global existence of solutions to 1D transport equations with nonlocal velocity (with Hantaek Bae and Rafael Granero-Belinchon).
Networks & Heterogeneous Media, 14 (3) : 471-487. (2019)
Regularity results for a class of generalized surface quasi-geostrophic equations (with Liutang Xue).
Journal de Mathématiques Pures et Appliquées, 130, 200-250 (2019).
Growth in the Muskat problem (with Rafael Granero-Belinchon).
Math. Model. Nat. Phenom., Volume 15, 1-23, (2020).
Paralinearization of the Muskat equation and application to the Cauchy problem (with Thomas Alazard).
Arch. Ration. Mech. Anal., 237, 545-583 (2020).
Global well-posedness for the 2D stable Muskat problem in H^3/2 (with Diego Cordoba).
Ann. Sci. Éc. Norm. Supér., 54(4): 1315-1351, (2021).
On the dynamics of the roots of polynomials under differentiation (with Thomas Alazard and Quoc-Hung Nguyen).
Journal de Mathématiques Pures et Appliquées, 162, 1-22 (2022)
Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space (with Francisco Gancedo)
Arch. Ration. Mech. Anal., 246, 141-207 (2022)
On the regularity of temperature fronts for the 3D viscous Boussinesq system (with Yatao Li and Liutang Xue),
Indiana. Univ. Math, J., no3, 1005-1060 (2024)
Global regularity and infinite Prandtl number limit of temperature patches for the 2D Boussinesq system (with Liutang Xue and Jiakun Yang),
Math. Ann. 392, 1375–1446 (2025).
Global well-posedness and density patches for liquid crystal system (with Qionglei Chen and Xiaonan Hao),
Journal of Functional Analysis, 290, no8, 55 pp. (2026)
Other publications (lecture notes, conference proceedings)
[lecture notes] Small scale creation in inviscd fluids - in Transport Fluid and Mixing (with Mikhail Chernobay, Alexander Kiselev and Chao Li), Partial Differ. Equ. Meas. Theory, De Gruyter Open, Warsaw, (2017), pp 95-117.