Vlad Vicol


Google Scholar profile.
Most of my papers are available on the arXiv preprint server, though these may not be the latest versions of the papers.


Publications
  1. Jiajie Chen, Giorgio Cialdea, Steve Shkoller, Vlad Vicol.
    Vorticity blowup in 2D compressible Euler equations.
    arXiv:2407.06455 [math.AP] Submitted, 2024.

  2. Steve Shkoller, Vlad Vicol.
    The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions.
    Inventiones Mathematicae 237 (2024), no. 3, 871-1252.

  3. Bjorn Engquist, Panagiotis Souganidis, Samuel N. Stechmann, Vlad Vicol.
    In Memory of Andrew J. Majda.
    Notices of the American Mathematical Society 70 (2023), no. 10, 1648-1666.

  4. Scott Armstrong, Vlad Vicol.
    Anomalous diffusion by fractal homogenization.
    arXiv:2305.05048 [math.AP] Submitted, 2023.

  5. Isaac Neal, Calum Rickard, Steve Shkoller, Vlad Vicol.
    A new type of stable shock formation in gas dynamics.
    Communications on Pure and Applied Analysis 23 (2024), no. 10, 1423-1447.

  6. Isaac Neal, Steve Shkoller, Vlad Vicol.
    A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy.
    arXiv:2302.01289 [math.AP] Submitted, 2023.

  7. [BOOK] Jacob Bedrossian, Vlad Vicol.
    The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction.
    AMS Graduate Studies in Mathematics 225 (2022), 218 pp.

  8. Tristan Buckmaster, Theodore Drivas, Steve Shkoller, Vlad Vicol.
    Formation and development of singularities for the compressible Euler equations.
    Proceedings of the International Congress of Mathematicians 2022, vol. 5, 3636-3659. EMS Press, Berlin, 2023.

  9. Matthew Novack, Vlad Vicol.
    An intermittent Onsager theorem.
    Inventiones Mathematicae 233 (2023), no. 1, 223-323.

  10. Igor Kukavica, Matthew Novack, Vlad Vicol.
    Exact Boundary Controllability for the Ideal Magneto-hydrodynamic Equations.
    Journal of Differential Equations 318 (2022), 94-112.

  11. Igor Kukavica, Trinh Nguyen, Vlad Vicol, Fei Wang.
    On the Euler+Prandtl expansion for the Navier-Stokes equations.
    Journal of Mathematical Fluid Mechanics 24:47 (2022).

  12. Tristan Buckmaster, Theodore D. Drivas, Steve Shkoller, Vlad Vicol.
    Simultaneous development of shocks and cusps for 2D Euler with azimuthal symmetry from smooth data.
    Annals of PDE 8, 26 (2022).

  13. Rajendra Beekie, Susan Friedlander, Vlad Vicol.
    On Moffatt’s magnetic relaxation equations.
    Communications in Mathematical Physics 390 (2022), 1311-1339.

  14. Alexey Cheskidov, Nathan Glatt-Holtz, Natasa Pavlovic, Roman Shvydkoy, Vlad Vicol.
    Susan Friedlander's contributions in mathematical fluid dynamics.
    Notices of the American Mathematical Socciety 68 (2021), no. 3, 331–343.

  15. Tristan Buckmaster, Nader Masmoudi, Matthew Novack, Vlad Vicol.
    Non-conservative H^{1/2-} weak solutions of the incompressible 3D Euler equations. arXiv:2101.09278 [math.AP].
    Intermittent Convex Integration for the 3D Euler Equations. Annals of Mathematics Studies, Vol. 217, 2023.

  16. Tristan Buckmaster, Vlad Vicol.
    Convex integration constructions in hydrodynamics.
    Bulletin of the AMS 58 (2021), no. 1, 1-44.

  17. Tristan Buckmaster, Steve Shkoller, Vlad Vicol.
    Shock formation and vorticity creation for 3d Euler.
    Communications on Pure and Applied Mathematics 76 (2023), no. 9, 1965–2072.

  18. Igor Kukavica, Vlad Vicol, Fei Wang.
    Remarks on the inviscid limit problem for the Navier-Stokes equations.
    Pure and Applied Functional Analysis 7 (2022), no. 1, 283-306. To the memory of Ciprian Foias.

  19. Tristan Buckmaster, Steve Shkoller, Vlad Vicol.
    Formation of point shocks for 3D compressible Euler.
    Communications on Pure and Applied Mathematics, 76 (2023), no. 9, 2073–2191.

  20. Rajendra Beekie, Tristan Buckmaster, Vlad Vicol.
    Weak solutions of ideal MHD which do not conserve magnetic helicity.
    Annals of PDE 6 (2020), no. 1, Paper No. 1, 40 pp.

  21. Tristan Buckmaster, Steve Shkoller, Vlad Vicol.
    Formation of shocks for 2D isentropic compressible Euler.
    Communications on Pure and Applied Mathematics 75 (2022), no. 9, 2069-2120.

  22. Sameer Iyer, Vlad Vicol.
    Real analytic local well-posedness for the Triple Deck.
    Communications on Pure and Applied Mathematics 8 (2021), no. 8, 1641-1684.

  23. Igor Kukavica, Vlad Vicol, Fei Wang.
    The inviscid limit for the Navier-Stokes equations with data analytic only near the boundary.
    Archive for Rational Mechanics and Analysis 237 (2020), no. 2, 779-827.

  24. Tristan Buckmaster, Vlad Vicol.
    A Heuristic Approach to Convex Integration for the Euler Equations.
    In: Berselli L.C., Ruzicka M. (eds) Progress in Mathematical Fluid Dynamics. Lecture Notes in Mathematics, vol 2272. Springer, Cham. 2020.

  25. Peter Constantin, Joonhyun La, Vlad Vicol.
    Remarks on a paper by Gavrilov: Grad-Shafranov equations, steady solutions of the three dimensional incompressible Euler equations with compactly supported velocities, and applications.
    Geometric and Functional Analysis 29 (2019), no. 6, 1773-1793.

  26. Tristan Buckmaster, Vlad Vicol.
    Convex integration and phenomenologies in turbulence.
    EMS Surveys in Mathematical Sciences 6 (2019), no. 1/2, 173-263.

  27. Guher Camliyurt, Igor Kukavica, Vlad Vicol.
    Analyticity up to the boundary for the Stokes and the Navier-Stokes systems.
    Transactions of the AMS 373 (2020), no. 5, 3375-3422.

  28. Peter Constantin, Milton Lopes Filho, Helena Nussenzveig Lopes, Vlad Vicol.
    Vorticity measures and the inviscid limit.
    Archive for Rational Mechanics and Analysis 234 (2019), no. 2, 575-593.

  29. Tristan Buckmaster, Maria Colombo, Vlad Vicol.
    Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1.
    Journal of the European Mathematical Society 24 (2022), no. 9, 3333-3378.

  30. David Gérard-Varet, Nader Masmoudi, Vlad Vicol.
    Well-posedness of the hydrostatic Navier-Stokes equations.
    Analysis and PDE, 13 (2020), no. 5, 1417–1455.

  31. Guher Camliyurt, Igor Kukavica, Vlad Vicol.
    Gevrey regularity of the Navier-Stokes equations in a half-space.
    Journal of Differential Equations 265 (2018), no. 9, 4052-4075.

  32. Igor Kukavica, Vlad Vicol.
    A direct approach to Gevrey regularity on the half-space.
    In volume: Partial Differential Equations in Fluid Mechanics. C.L. Fefferman, J.C. Robinson, and J.L. Rodrigo, eds. London Mathematical Society Lecture Note Series 452, (2018), 268-288.

  33. Jacob Bedrossian, Michele Coti Zelati, Vlad Vicol.
    Vortex axisymmetrization, inviscid damping, and vorticity depletion in the linearized 2D Euler equations.
    Annals of PDE 5 (2019), no. 4, 1-192.

  34. Tristan Buckmaster, Vlad Vicol.
    Nonuniqueness of weak solutions to the Navier-Stokes equation.
    Annals of Mathematics 189 (2019), no. 1, 101-144.

  35. Peter Constantin, Tarek Elgindi, Huy Nguyen, Vlad Vicol.
    On singularity formation in a Hele-Shaw model.
    Communications in Mathematical Physics 363 (2018), no. 1, 139-171.

  36. Peter Constantin, Vlad Vicol.
    Remarks on high Reynolds numbers hydrodynamics and the inviscid limit.
    Journal of Nonlinear Science 28 (2018), no. 2, 711-724.

  37. Tristan Buckmaster, Camillo De Lellis, László Székelyhidi Jr., Vlad Vicol.
    Onsager's conjecture for admissible weak solutions.
    Communications on Pure and Applied Mathematics 72 (2019), no. 2, 229-274.

  38. Tristan Buckmaster, Steve Shkoller, Vlad Vicol.
    Nonuniqueness of weak solutions to the SQG equation.
    Communications on Pure and Applied Mathematics 72 (2019), no. 9, 1809-1874.

  39. Jacob Bedrossian, Vlad Vicol, Fei Wang.
    The Sobolev stability threshold for 2D shear flows near Couette.
    Journal of Nonlinear Science 28 (2018), no. 6, 2051-2075.

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

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

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

  43. Peter Constantin, Tarek Elgindi, Mihaela Ignatova, Vlad Vicol.
    On some electroconvection models.
    Journal of Nonlinear Science 27 (2017), no. 1, 197-211.

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

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

  46. Peter Constantin, Michele Coti Zelati, Vlad Vicol.
    Uniformly attracting limit sets for the critically dissipative SQG equation.
    Nonlinearity 29 (2016), no. 2, 298-318.

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

  48. Igor Kukavica, Amjad Tuffaha, Vlad Vicol.
    On the local existence for the 3D Euler equation with a free interface.
    Applied Mathematics and Optimization 76 (2017), no. 3, 535-563.

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

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

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

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

  53. Phillip Isett, Vlad Vicol.
    Holder continuous solutions of active scalar equations.
    Annals of PDE 1 (2015), no. 1, 1-77.

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

  55. Peter Constantin, Vlad Vicol, Jiahong Wu.
    Analyticity of Lagrangian trajectories for well-posed inviscid incompressible fluid models.
    Advances in Mathematics 285 (2015), 352-393.

  56. Peter Constantin, Igor Kukavica, Vlad Vicol.
    On the inviscid limit of the Navier-Stokes equations.
    Proceedings of the American Mathematical Society 143 (2015), no. 7, 3075-3090.

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

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

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

  60. Peter Constantin, Andrei Tarfulea, Vlad Vicol.
    Long time dynamics of forced critical SQG.
    Communications in Mathematical Physics 335 (2015), no. 1, 93-141.

  61. Peter Constantin, Andrei Tarfulea, Vlad Vicol.
    Absence of anomalous dissipation of energy in forced two dimensional fluid equations.
    Archive for Rational Mechanics and Analysis 212 (2014), no. 3, 875-903.

  62. Peter Constantin, Nathan Glatt-Holtz, Vlad Vicol.
    Unique ergodicity for fractionally dissipated, stochastically forced 2D Euler equations.
    Communications in Mathematical Physics 330 (2014), no. 2, 819-857.

  63. Susan Friedlander, Walter Rusin, Vlad Vicol.
    The magneto-geostrophic equations: a survey.
    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.

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

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

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

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

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

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

  70. Susan Friedlander, Walter Rusin, Vlad Vicol.
    On the supercritically diffusive magneto-geostrophic equations.
    Nonlinearity, 25 (2012), no. 11, 3071-3097.

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

  72. Michael Dabkowski, Alexander Kiselev, Vlad Vicol.
    Global well-posedness for a slightly supercritical surface quasi-geostrophic equation.
    Nonlinearity 25 (2012), no. 5, 1525-1535.

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

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

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

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

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

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

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

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

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

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

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

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

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