Vlad Vicol



My Google Scholar profile may be found here.
Most of my papers are also available on the arXiv preprint server (these though may not be the latest versions of the papers). Click here to access them.



Publications
  1. On singularity formation in a Hele-Shaw model. (with Peter Constantin, Tarek Elgindi, Huy Nguyen) Submitted, 2017. arXiv:1708.08490 [math.AP] (pdf)

  2. Remarks on high Reynolds numbers hydrodynamics and the inviscid limit. (with Peter Constantin) Submitted, 2017. arXiv:1708.03225 [math.AP] (pdf)

  3. Onsager's conjecture for admissible weak solutions. (with Tristan Buckmaster, Camillo De Lellis, László Székelyhidi Jr.) Submitted, 2017. arXiv:1701.08678 [math.AP] (pdf)

  4. Nonuniqueness of weak solutions to the SQG equation. (with Tristan Buckmaster and Steve Shkoller) Submitted, 2016. arXiv:1610.00676 [math.AP] (pdf)

  5. The Sobolev stability threshold for 2D shear flows near Couette. (with Jacob Bedrossian and Fei Wang) Journal of Nonlinear Science, Accepted, (2016). DOI: 10.1007/s00332-016-9330-9. (pdf)

  6. On the existence for the free interface 2D Euler equation with a localized vorticity condition. (with Igor Kukavica, Amjad Tuffaha, and Fei Wang) Applied Math and Optimization 73 (2016), no. 3, 523-544. To the memory of Professor A.V. Balakrishnan. (pdf)

  7. The van Dommelen and Shen singularity in the Prandtl equations. (with Igor Kukavica and Fei Wang) Advances in Mathematics 307 (2017), 288-311. (pdf)

  8. Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields. (with Peter Constantin, Tarek Elgindi, and Mihaela Ignatova) SIAM Journal on Mathematical Analysis 49 (2017), no. 3, 1932-1946. (pdf)

  9. On some electroconvection models. (with Peter Constantin, Tarek Elgindi, and Mihaela Ignatova) Journal of Nonlinear Science 27 (2017), no. 1, 197-211. (pdf)

  10. On the ill-posedness of active scalar equations with odd singular kernels. (with Igor Kukavica and Fei Wang) New Trends in Differential Equations, Control Theory and Optimization: Proceedings of the Eighth Congress of Romanian Mathematicians (2016), 185-200. (pdf)

  11. Global regularity for 2D Muskat equations with finite slope. (with Peter Constantin, Francisco Gancedo, and Roman Shvydkoy) Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 34 (2017), no. 4, 1041-1074. (pdf)

  12. Uniformly attracting limit sets for the critically dissipative SQG equation. (with Peter Constantin and Michele Coti Zelati) Nonlinearity 29 (2016), no. 2, 298-318. (pdf)

  13. Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations. (with Peter Constantin and Igor Kukavica) Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 33 (2016), no. 6, 1569-1588. (pdf)

  14. On the local existence for the 3D Euler equation with a free interface. (with Igor Kukavica and Amjad Tuffaha) Applied Mathematics and Optimization, Accepted, (2016). DOI: 10.1007/s00245-016-9360-6. (pdf)

  15. Almost global existence for the Prandtl boundary layer equations. (with Mihaela Ignatova) Archive for Rational Mechanics and Analysis 220 (2016), no. 2, 809-848. (pdf)

  16. On the global regularity for the supercritical SQG equation. (with Michele Coti Zelati) Indiana University Mathematics Journal 65 (2016), no. 2, 535-552. (pdf)

  17. Enhanced dissipation and inviscid damping in the inviscid limit of the Navier-Stokes equations near the 2D Couette flow. (with Jacob Bedrossian and Nader Masmoudi) Archive for Rational Mechanics and Analysis 219 (2016), no. 3, 1087-1159. (pdf)

  18. On a transport equation with nonlocal drift. (with Luis Silvestre) Transactions of the American Mathematical Society 368 (2016), no. 9, 6159-6188. (pdf)

  19. Holder continuous solutions of active scalar equations. (with Phillip Isett) Annals of PDE 1 (2015), no. 1, 1-77. (pdf)

  20. Inviscid limits for a stochastically forced shell model of turbulent flow. (with Susan Friedlander and Nathan Glatt-Holtz) Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 52 (2016), no. 3, 1217-1247. (pdf)

  21. Analyticity of Lagrangian trajectories for well-posed inviscid incompressible fluid models. (with Peter Constantin and Jiahong Wu) Advances in Mathematics 285 (2015), 352-393. (pdf)

  22. On the inviscid limit of the Navier-Stokes equations. (with Peter Constantin and Igor Kukavica) Proceedings of the American Mathematical Society 143 (2015), no. 7, 3075-3090. (pdf)

  23. On the local well-posedness of the Prandtl and the hydrostatic Euler equations with multiple monotonicity regions. (with Igor Kukavica, Nader Masmoudi, and Tak Kwong Wong) SIAM Journal of Mathematical Analysis 46 (2014), no. 6, 3865-3890. (pdf)

  24. Existence and regularity of invariant measures for the three dimensional stochastic primitive equations. (with Nathan Glatt-Holtz, Igor Kukavica, and Mohammed Ziane) Journal of Matematical Physics 55, 051504 (2014). (pdf)

  25. On inviscid limits for the stochastic Navier-Stokes equations and related models. (with Nathan Glatt-Holtz and Vladimír Šverák) Archive for Rational Mechanics and Analysis 217 (2015), no. 2, 619-649. (pdf)

  26. Long time dynamics of forced critical SQG. (with Peter Constantin and Andrei Tarfulea) Communications in Mathematical Physics 335 (2015), no. 1, 93-141. (pdf)

  27. Absence of anomalous dissipation of energy in forced two dimensional fluid equations. (with Peter Constantin and Andrei Tarfulea) Archive for Rational Mechanics and Analysis 212 (2014), no. 3, 875–903. (pdf)

  28. Unique ergodicity for fractionally dissipated, stochastically forced 2D Euler equations. (with Peter Constantin and Nathan Glatt-Holtz) Communications in Mathematical Physiscs 330 (2014), no. 2, 819-857. (pdf)

  29. The magneto-geostrophic equations: a survey. (with Susan Friedlander and Walter Rusin) Proceedings of the St. Petersburg Mathematical Society, Volume XV: Advances in Mathematical Analysis of Partial Differential Equations. (2014) D. Apushkinskaya, and A.I. Nazarov, eds. pp. 53–78. (pdf)

  30. On moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain. (with Igor Kukavica) Asymptotic Analysis 90 (2014), no. 3-4, 189-206. (pdf)

  31. Global well-posedness of slightly supercritical active scalar equations. (with Michael Dabkowski, Alexander Kiselev, and Luis Silvestre) Analysis and PDE 7 (2014), no. 1, 43-72. (pdf)

  32. Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise. (with Nathan Glatt-Holtz) The Annals of Probability 42 (2014), no. 1, 80-145. (pdf)

  33. On the loss of continuity for super-critical drift-diffusion equations. (with Luis Silvestre and Andrej Zlatoš) Archive for Rational Mechanics and Analysis 207 (2013), no. 3, 845-877. (pdf)

  34. On the local existence of analytic solutions to the Prandtl boundary layer equations. (with Igor Kukavica) Communications in Mathematical Sciences 11 (2013), no. 1, 269-292. (pdf)

  35. On a singular incompressible porous media equation. (with Susan Friedlander, Francisco Gancedo, and Weiran Sun) Journal of Mathematical Physics 53 (2012), no. 11, 115602, 1--20. Special Issue "Incompressible Fluids, Turbulence and Mixing" in honor of Peter Constantin. (pdf)

  36. On the supercritically diffusive magneto-geostrophic equations. (with Susan Friedlander and Walter Rusin) Nonlinearity, 25 (2012), no. 11, 3071-3097. (pdf)

  37. Nonlinear maximum principles for dissipative linear nonlocal operators and applications. (with Peter Constantin) Geometric and Functional Analysis, 22 (2012), no. 5, 1289-1321. (pdf)

  38. Global well-posedness for a slightly supercritical surface quasi-geostrophic equation. (with Michael Dabkowski and Alexander Kiselev) Nonlinearity 25 (2012), no. 5, 1525-1535. (pdf)

  39. Hölder continuity for a drift-diffusion equation with pressure. (with Luis Silvestre) Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 29 (2012), no. 4, 637-652. (pdf)

  40. On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations. (with Susan Friedlander) Nonlinearity 24 (2011), no. 11, 3019-3042. (pdf)

  41. Higher regularity of Holder continuous solutions of parabolic equations with singular drift velocities. (with Susan Friedlander) Journal of Mathematical Fluid Mechanics 14 (2012), no. 2, 255-266. (pdf)

  42. Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics. (with Susan Friedlander) Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 28 (2011), no. 2, 283-301. (pdf)

  43. Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain. (with Igor Kukavica, Roger Temam, and Mohammed Ziane) Journal of Differential Equations 250 (2011), 1719-1746. (pdf)

  44. On the analyticity and Gevrey-class regularity up to the boundary for the Euler Equations. (with Igor Kukavica) Nonlinearity 24 (2011), no. 3, 765-796. (pdf)

  45. Analyticity and Gevrey-class regularity for the second-grade fluid equations. (with Marius Paicu) Journal of Mathematical Fluid Mechanics 13 (2011), no. 4, 533-555. (pdf)

  46. The domain of analyticity of solutions to the three-dimensional Euler equations in a half space. (with Igor Kukavica) Discrete and Continuous Dynamical Systems 29 (2011), no. 1, 285-303. (pdf)

  47. Existence and uniqueness of solutions for the hydrostatic Euler equations on a bounded domain with analytic data. (with Igor Kukavica, Roger Temam, and Mohammed Ziane) Comptes Rendus Mathematique 348 (2010), no. 11-12, 639-645. (pdf)

  48. Nonlinear instability for the critically dissipative quasi-geostrophic equation. (with Susan Friedlander and Nataša Pavlović) Communications in Mathematical Physics 292 (2009), no. 3, 797-810. (pdf)

  49. On the radius of analyticity of solutions to the three-dimensional Euler equations. (with Igor Kukavica) Proceedings of the American Mathematical Society 137 (2009), no. 2, 669-677. (pdf)

  50. On local uniqueness of weak solutions to the Navier-Stokes system with BMO-1 initial datum. (with Igor Kukavica) Journal of Dynamics and Differential Equations 20 (2008), no. 3, 719-732. (pdf)

  51. A combinatorial classification of postsingularly finite complex exponential maps. (with Bastian Laubner and Dierk Schleicher) Discrete and Continuous Dynamical Systems 22 (2008), no. 3, 663-682. (pdf)