I am 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: x.y@nyu.edu, where x=omar and y=lazar
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)
One 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 unique solvability and the relation of density patches for liquid crystal system (with Qionglei Chen and Xiaonan Hao), 36p
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.