Publications

with David Ambrose and Milton C. Lopes Filho. Improved regularity and analyticity of Cannone-Karch solutions of the three-dimensional Navier-Stokes equations on the torus. Monatsh. Math. 206 (2025), 781–795. 

with David Ambrose and Milton C. Lopes Filho. Existence and analyticity of solutions of the Kuramoto-Sivashinsky equation with singular data. Proc. Royal Soc. Edinburgh. Section A, Mathematics, Published online https://doi.org/10.1017/prm.2024.106 (2025).

with David Ambrose and Milton C. Lopes Filho. Existence and analyticity of the Lei-Lin solution of the Navier-Stokes equations on the torus. Proc. Amer. Math. Soc., 152 (2023), 781–795.

with A. Valentina Busuioc, Dragos Iftimie and Milton C. Lopes Filho. The incompressible α–Euler equations in the exterior of a vanishing disk, Indiana Univ. Math. J., 73 (2024), 691–721. 

with Milton C. Lopes Filho. Energy balance for forced two-dimensional incompressible ideal fluid flow. Phil. Trans. R. Soc. A, 380 (2022), 20210095.    https://doi.org/10.1098/rsta.2021.0095 (2022).

with Christian Seis and Emil Wiedemann. On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity. Nonlinearity, 34 (2021), 3112–3121. 

with A. Valentina Busuioc, Dragos Iftimie and Milton C. Lopes Filho. The limit α → 0 of the α-Euler equations in the half-plane with no-slip boundary conditions and vortex sheet initial data. SIAM J Math Analysis. 52 (2020), 5257–5286.

with Dragos Iftimie and Milton C. Lopes Filho. Weak vorticity formulation of the incompressible 2D Euler equations in bounded domains. Comm Partial Diff Equations, 45 (2020), 109–145.

with Peter Constantin, Milton C. Lopes Filho and Vlad Vicol. Vorticity measures and vanishing viscosity. Archive Rat Mech Anal. 234 (2019), 575–593.

with Gung-Min Gie, J.P. Kelliher, M.C. Lopes Filho and A.L. Mazzucato. The vanishing viscosity limit for some symmetric flows. Ann. Instit. Henri Poincaré C, Analyse non linéaire. 36 (2019), 1237–1280.

with David Ambrose and Milton C. Lopes Filho. Confinement of vorticity for the 2D Euler-alpha equations. Journal of Differential Equations, 265 (2018), 5472–5489.

with Christophe Lacave and Milton C. Lopes Filho. Asymptotic behavior of incompressible ideal flow around small disks. Asymptotic Analysis, v. 108, no. 1-2, (2018), 45–83.

with Quansen Jiu, Dongjuan Niu and Milton C. Lopes Filho. The limit of vanishing viscosity for the incompressible 3D Navier-Stokes equations with helical symmetry. Physica D: Nonlinear Phenomena, 376, (2018) 238–246. Special Issue in Honor of  Edriss S. Titi’s 60th Birthday.

with Alexey Cheskidov, Milton C. Lopes Filho and Roman Shvydkoy. Energy conservation in two-dimensional incompressible ideal fluids. Communications in Mathematical Physics, 348(1), (2016) 129–143. 

with A. Valentina Busuioc, Dragos Iftimie and Milton C. Lopes Filho. Uniform time of existence for the α–Euler equations. Journal of Functional Analysis, 271 (2016), 1341–1375.

with D. A. F. Albanez and E. S. Titi. Continuous data assimilation for the three-dimensional Navier-Stokes-α model. Asymptotic Analysis, 97 (2016), 139–164.

with Gianluca Crippa, Milton C. Lopes Filho and Evelyne Miot. Flows of vector fields with point singularities and the vortex-wave system. Discrete and Continuous Dynamical Systems. v.36, (2016) 2405–2417.

with David Ambrose, James P. Kelliher and Milton C. Lopes Filho. Serfati solutions to the 2D Euler equations on exterior domains, J. Diff. Equations, 259 (2015), 4509–4560.

with M.C. Lopes Filho, E. S. Titi and Aibin Zang. Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary Conditions. Journal of Mathematical Fluid Mechanics (Printed Ed.). , v.17, (2015) 327–340.

with Anne C. Bronzi and Milton C. Lopes Filho.  Global existence of a weak solution of the incompressible Euler equations with helical symmetry and  vorticity. Indiana University Mathematics Journal 64 (2015), 309–341.

with Anne C. Bronzi and Milton C. Lopes Filho.   Wild solutions for 2D incompressible ideal flow with passive tracer. Commun. in Math. Sci. 13 (2015), 1333–1343.

with Milton C. Lopes Filho,  Edriss S. Titi and Aibin Zang.  Convergence of the 2D Euler–α to Euler equations in the Dirichlet case: indifference to boundary layers. Phys. D 292(293) (2015), 51–61.    

with Milton C. Lopes Filho, Anna L. Mazzucato, Dongjuan Niu and Edriss S. Titi. Planar Limits of Three-Dimensional Incompressible Flows with Helical Symmetry. Journal of Dynamics and Differential Equations. 26 (2014), 843–869.

with Geoffrey R. Burton and Milton C. Lopes Filho. Nonlinear stability for steady vortex pairs. Communications Math. Phys. 324 (2013), 445–463.

with Milton C. Lopes Filho and Huy Hoang Nguyen. Incompressible and ideal 2D flow around a small obstacle with constant velocity at infinity. Quarterly of Applied Mathematics. 71 (2013) 679–687.

with Claude Bardos, Milton  Lopes Filho, Dongjuan Niu and Edriss S. Titi. Stability of two-dimensional viscous incompressible flows under three-dimensional perturbations and inviscid symmetry breaking. SIAM J. Math. Anal. 45 (2013), no. 3, 1871–1885. 

with A. Valentina Busuioc, Dragos Iftimie and Milton C. Lopes Filho.   Incompressible Euler as a limit of complex fluid models with Navier boundary conditions. J. Differential Equations 252 (2012), no. 1, 624–640. 

with Milton C. Lopes Filho and Evelyne Miot.  Existence of a weak solution in to the vortex-wave system. J. Nonlinear Sci. 21 (2011), no. 5, 685–703. 

with Milton C. Lopes Filho and Juliana C. Precioso.   Least action principle and the incompressible Euler equations with variable density. Trans. Amer. Math. Soc. 363 (2011), no. 5, 2641–2661. 

with David M. Ambrose, Milton C. Lopes Filho and Walter A. Strauss.   Transport of interfaces with surface tension by 2D viscous flows. Interfaces Free Bound. 12 (2010), no. 1, 23–44. 

with Milton C. Lopes Filho. Vortex dynamics on a domain with holes. In: IUTAM symposium, Copenhagen. Theoretical and Computational Fluid Dynamics. Berlin: Springer Verlag, 24 (2010) 51–57.

with James P. Kelliher and Milton C. Lopes Filho. Vanishing viscosity limit for an expanding domain in space. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, 2521–2537. 

with Josiane C. O. Faria and Milton C. Lopes Filho.  Weak stability of Lagrangian solutions to the semigeostrophic equations. Nonlinearity 22 (2009), no. 10, 2521–2539. 

with Dragos Iftimie and Milton C. Lopes Filho. Incompressible flow around a small obstacle and the vanishing viscosity limit. Comm. Math. Phys. 287 (2009), no. 1, 99–115. 

with Milton C. Lopes Filho, Anna L. Mazzucato, and Michael Taylor. Vanishing viscosity limits and boundary layers for circularly symmetric 2D flows. Bull. Braz. Math. Soc. (N.S.) 39 (2008), no. 4, 471–513.  

with Anne C. Bronzi and Milton C. Lopes Filho. Computational visualization of Shnirelman’s compactly supported weak solution. In: Euler equations: 250 years on, 2007, Aussois. Physica D, special issue, Euler equations: 250 years on. New York: Elsevier, (2008). 

with Milton C. Lopes Filho and Anna L. Mazzucato.   Vanishing viscosity limit for incompressible flow inside a rotating circle. Phys. D 237 (2008), no. 10-12, 1324–1333.   

with Dragos Iftimie and Milton C. Lopes Filho. Confinement of vorticity in two dimensional  ideal incompressible exterior flow. Quarterly of Applied Mathematics. 65, (2007) 499–521.

with Milton C. Lopes Filho and Steven Schochet.  A criterion for the equivalence of the Birkhoff-Rott and Euler descriptions of vortex sheet evolution. Trans. Amer. Math. Soc. 359 (2007), no. 9, 4125–4142 (electronic). 

with Milton C. Lopes Filho and Zhouping Xin.  Vortex sheets with reflection symmetry in exterior domains. J. Differential Equations 229 (2006), no. 1, 154–171. 

with Dragos Iftimie and Milton C. Lopes Filho.  Two-dimensional incompressible viscous flow around a small obstacle. Math. Ann. 336 (2006), no. 2, 449–489. 

with Milton C. Lopes Filho, John Lowengrub and Yuxi Zheng.  Numerical evidence of nonuniqueness in the evolution of vortex sheets. M2AN Math. Model. Numer. Anal. 40 (2006), no. 2, 225–237. 

with Milton C. Lopes Filho and Anna L. Mazzucato.  Weak solutions, renormalized solutions and enstrophy defects in 2D turbulence. Arch. Ration. Mech. Anal. 179 (2006), no. 3, 353–387.

with Milton C. Lopes Filho and Gabriela Planas.  On the inviscid limit for two-dimensional incompressible flow with Navier friction condition. SIAM J. Math. Anal. 36 (2005), no. 4, 1130–1141 (electronic).

with Dragos Iftimie  and Milton C. Lopes Filho.  Large time behavior for vortex evolution in the half-plane. Comm. Math. Phys. 237 (2003), no. 3, 441–469. 

with Dragos Iftimie  and Milton C. Lopes Filho. On the large-time behavior of two-dimensional vortex dynamics. Phys. D 179 (2003), no. 3-4, 153–160. 

with Milton C. Lopes Filho and Max O. Souza.  On the equation satisfied by a steady Prandtl-Munk vortex sheet. Commun. Math. Sci. 1 (2003), no. 1, 68–73.  

with Dragos Iftimie  and Milton C. Lopes Filho. Two dimensional incompressible ideal flow around a small obstacle. Comm. Partial Differential Equations 28 (2003), no. 1-2, 349–379.    

with Milton C. Lopes Filho. Existence of weak solutions to the semigeostrohic equation with integrable initial data. Proceedings of the Royal Society of Edinburgh. Section A, Mathematics. 132 (2002) 329–339.

with Dragos Iftimie and Milton C. Lopes Filho. Comportement en temps grand pour les ecoulements parfaits incompressibles dans un demi-plan. In: Séminaire Équations aux Derivées Partielles, Ec. Polytechnique, 2002, Palaiseu.  v. 2001-2. p. 1–8. 

with Milton C. Lopes Filho, Pointwise blow-up of sequences bounded in L1. Journal of Mathematical Analysis and Applications. 263 (2001) 447–454.

with Milton C. Lopes Filho and Zhouping  Xin.   Existence of vortex sheets with reflection symmetry in two space dimensions. Arch. Ration. Mech. Anal. 158 (2001), no. 3, 235–257.

with Milton C. Lopes Filho and Eitan Tadmor.   Approximate solutions of the incompressible Euler equations with no concentrations. Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000), no. 3, 371–412. 

with Jorge Hounie and Milton C. Lopes Filho.   Bounds on the dispersion of vorticity in 2D incompressible, inviscid flows with a priori unbounded velocity. SIAM J. Math. Anal. 31 (1999), no. 1, 134–153. 

with Milton C. Lopes Filho and Yuxi Zheng.   Weak solutions for the equations of incompressible and inviscid fluid dynamics. 22o Colóquio Brasileiro de Matemática. [22nd Brazilian Mathematics Colloquium] Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 1999.   

with Milton C. Lopes Filho. Propagation Of Support And Singularity Formation For A Class Of 2D Quasilinear Hyperbolic Systems. Quarterly of Applied Mathematics. 57 (1999)  229–243.

with Milton C. Lopes Filho and Yuxi Zheng. Convergence of the vanishing viscosity approximation for superpositions of confined eddies. Comm. Math. Phys. 201 (1999), no. 2, 291–304.   

with Milton C. Lopes Filho, Jorge Hounie and Steven Schochet. A Priori Temporal Regularity For The Stream Function Of 2d Incompressible, Inviscid Flow. Nonlinear Analysis. Theory, Methods and Applications. 35 (1999) 871–884.

with Milton C. Lopes Filho. An extension of Marchioro's bound on the growth of a vortex patch to flows with Lp  vorticity. SIAM J. Math. Anal. 29 (1998), no. 3, 596–599 (electronic).   

with Jorge Hounie, Milton C. Lopes Filho and Steven Schochet. A Priori Estimates For The Stream Function Of 2D Incompressible, Inviscid Fluid. In: II World Congress of Nonlinear Analysts, 1997, Atenas. Nonlinear Analysis: Theory, Methods and Applications. Elsevier Science, 30 (1997) 5053–5058.

with David R. Adams. Nonlinear Weakly Elliptic 2x2 Systems Of Variational Inequalities With Unilateral Obstacle Constraints. Electronic Journal of Differential Equations. 1997 (1997) 1–20. 1997.

A refined estimate of the size of concentration sets for 2D incompressible inviscid flow. Indiana Univ. Math. J. 46 (1997), no. 1, 165–182.  

with Milton C. Lopes Filho. Concentration Sets For 2d Incompressible Flow. In: III International Congress of Industrial and Applied Mathematics, 1996, Hamburg. ZAMM. Hamburg, Alemanha, 1996. v. 76. p. 101–104.

with Milton C. Lopes Filho. Smooth Solutions Of Partially Aligned Systems. In: III International Congress of Industrial and Applied Mathematics, 1996, Hamburg. ZAMM, 1996. v. 76. p. 141–144.

with Milton C. Lopes Filho. Singularity Formation For A System Of Conservation Laws In Two Space Dimensions. Journal of Mathematical Analysis and Applications. 200 (1996) 538–547.

with David R. Adams.   Weakly elliptic systems of variational inequalities: a 2 x 2 model problem with obstacles in both components. Ann. Mat. Pura Appl. (4) 169 (1995), 183–201.  

with Milton C. Lopes Filho. Multidimensional Hyperbolic Systems With Degenerate Characteristic Structure. In: III Workshop em EDP, 1993, Rio de Janeiro. Matematica Contemporanea. Rio de Janeiro: Soc. Bras. de Matematica, 8 (1995) 225–238.

An estimate on the Hausdorff dimension of a concentration set for the incompressible 2–D Euler equations. Indiana Univ. Math. J. 43 (1994), no. 2, 521–534.