• (with A. Zlatos) On discrete models of the Euler equation, pdf, IMRN 38 (2005) 2315--2339.


  • (with F. Nazarov and A. Volberg) Global well-posedness for the critical 2D dissipative quasi-geostrophic equation, pdf, Inventiones Math. 167 (2007) 445--453.


  • (with F. Nazarov and R. Shterenberg) Blow up and regularity for fractal Burgers equation, pdf, Dyn. Partial Differ. Equ. 5 (2008), no. 3, 211--240.


  • (with F. Nazarov) Global Regularity for the Critical Dispersive Dissipative Surface Quasi-Geostrophic Equation, pdf, Nonlinearity 23 (2010), 549--554.


  • (with F. Nazarov) A variation on a theme of Caffarelli and Vasseur, pdf, Zap. Nauchn. Sem. POMI 370 (2009), 58--72.


  • Some recent results on the critical surface quasi-geostrophic equation: a review pdf, Hyperbolic problems: theory, numerics and applications, 105--122, Proc. Sympos. Appl. Math., 67, Part 1, AMS, Providence, RI, 2009.


  • Regularity and blow up for active scalars, pdf, Math. Model. Math. Phenom. 5 (2010), 225--255.


  • (with F. Nazarov) A simple energy pump for the surface quasi-geostrophic equation, pdf, in Nonlinear Partial Differential Equations, Proceedings of the Abel Symposium 2010, Helge Holden and Kenneth Karlsen, Editors.


  • Nonlocal maximum principles for active scalars, pdf, Adv. Math. 227 (2011), 1806--1826.


  • (with M. Dabkowski and V. Vicol) Global well-posedness for a slightly supercritical surface quasi-geostrophic equation, pdf, Nonlinearity 25 (2012), no. 5, 1525--1535


  • (with M. Dabkowski, L. Silvestre and V. Vicol) Global well-posedness of slightly supercritical active scalar equations, pdf, Analysis and PDE 7 (2014), no. 1, 43–-72


  • (with V. Sverak) Small scale creation for solutions of the incompressible two dimensional Euler equation, pdf, Annals of Math, 180 (2014), 1205--1220


  • (with K. Choi and Y. Yao) Finite time blow up for a 1D model of 2D Boussinesq system, pdf, Comm. Math. Phys. 334 (2015), no. 3, 1667-–1679


  • (with K. Choi, T. Hou, G. Luo, V. Sverak and Y. Yao) On the finite time blow up of a 1D model for the 3D axisymmetric Euler equation, pdf, to appear at Commun. Pure and Applied Math.


  • (with A. Zlatos) Blow up for the 2D Euler equation on some bounded domains, pdf, J. Differential Equations 259 (2015), no. 7, 3490--3494


  • (with Y. Yao and A. Zlatos) Local regularity for the modified SQG patch equation, pdf, to appear at Commun. Pure and Applied Math.


  • (with L. Ryzhik, Y. Yao and A. Zlatos) Finite time singularity for the modified SQG patch equation, pdf, Annals of Math. 184 (2016), no. 3, 909--948


  • Small scale creation in viscid fluids, pdf, preprint, based on notes from Levico summer school taken by Omar Lazar, Chao Li, and Mikhail Chernobay.


  • (with T. Do and X. Xu) Stability of Blow Up for a 1D model of Axisymmetric 3D Euler Equation, pdf, preprint, to appear at J. Nonlinear Science.


  • (with C. Tan) Finite time blow up in the hyperbolic Boussinesq system, pdf, preprint.