Publications in reverse chronological order
(sorted by area here)
- The Euler equations in planar domains with corners (with C. Lacave),
- Universal mixers in all dimensions (with T. Elgindi),
- Stochastic homogenization for reaction-diffusion equations (with J. Lin),
Arch. Ration. Mech. Anal., to appear.
- Multidimensional transition fronts for Fisher-KPP reactions (with A. Alwan, Z. Han, J. Lin, and Z. Tao),
Nonlinearity, to appear.
- On the rate of merging of vorticity level sets for the 2D Euler equations,
J. Nonlinear Sci. 28 (2018), 2329-2341.
- A note on stability shifting for the Muskat problem II: From stable to unstable and back to stable (with D. Córdoba and J. Gómez-Serrano),
Anal. PDE 10 (2017), 367-378.
- Local regularity for the modified SQG patch equation (with A. Kiselev and Y. Yao),
Comm. Pure Appl. Math. 70 (2017), 12531315.
- Mixing and un-mixing by incompressible flows (with Y. Yao),
J. Eur. Math. Soc. 19 (2017), 1911-1948.
- Propagation of reactions in inhomogeneous media,
Comm. Pure Appl. Math. 70 (2017), 884-949.
- Existence and non-existence of transition fronts for bistable and ignition reactions,
Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), 1687-1705.
- Finite time singularity for the modified SQG patch equation (with A. Kiselev, L. Ryzhik, and Y. Yao),
Ann. of Math. 184 (2016), 909-948.
- Periodic orbits of the ABC flow with A=B=C=1 (with J. Xin and Y. Yu),
SIAM J. Math. Anal. 48 (2016), 4087-4093.
- Ballistic orbits and front speed enhancement for ABC flows (with T. McMillen, J. Xin, and Y. Yu),
SIAM J. Appl. Dyn. Syst. 15 (2016), 1753-1782.
- Transition fronts for inhomogeneous Fisher-KPP reactions and non-local diffusion (with T.S. Lim),
Trans. Amer. Math. Soc. 368 (2016), 8615-8631.
- Blow up for the 2D Euler equation on some bounded domains (with A. Kiselev),
J. Differential Equations 259 (2015), 3490-3494.
- Exponential growth of the vorticity gradient for the Euler equation on the torus,
Adv. Math. 268 (2015), 396-403.
- A note on stability shifting for the Muskat problem (with D. Córdoba and J. Gómez-Serrano),
Philos. Trans. A 373 (2015), 20140278.
- Transition fronts for inhomogeneous monostable reaction-diffusion equations via linearization at zero (with T. Tao and B. Zhu),
Nonlinearity 27 (2014), 2409-2416.
- On the loss of continuity for super-critical drift-diffusion equations (with L. Silvestre and V. Vicol),
Arch. Ration. Mech. Anal. 207 (2013), 845-877.
- The Harnack inequality for a class of degenerate elliptic operators (with F. Hamel),
Int. Math. Res. Notices 2013, 3732-3743.
- Speed-up of combustion fronts in shear flows (with F. Hamel),
Math. Ann. 356 (2013), 845-867.
- Generalized traveling waves in disordered media: Existence, uniqueness, and stability,
Arch. Ration. Mech. Anal. 208 (2013), 447-480.
- Transition fronts in inhomogeneous Fisher-KPP reaction-diffusion equations,
J. Math. Pures Appl. 98 (2012), 89-102.
- Existence and non-existence of Fisher-KPP transition fronts (with J. Nolen, J.-M. Roquejoffre, and L. Ryzhik),
Arch. Ration. Mech. Anal. 203 (2012), 217-246.
- On divergence-free drifts (with G. Seregin, L. Silvestre, and V. verák),
J. Differential Equations 252 (2012), 505-540.
- Reaction-diffusion front speed enhancement by flows,
Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), 711-726.
- Exit times of diffusions with incompressible drifts (with G. Iyer, A. Novikov, and L. Ryzhik),
SIAM J. Math. Anal. 42 (2010), 2484-2498.
- On the high intensity limit of interacting corpora (with P. Constantin),
Comm. Math. Sci. 8 (2010), 173-186.
- Diffusion in fluid flow: Dissipation enhancement by flows in 2D,
Comm. Partial Differential Equations 35 (2010), 496-534.
- Sharp asymptotics for KPP pulsating front speed-up and diffusion enhancement by flows,
Arch. Ration. Mech. Anal. 195 (2010), 441-453.
- Relaxation enhancement by time-periodic flows (with A. Kiselev and R. Shterenberg),
Indiana Univ. Math. J. 57 (2008), 2137-2152.
- Diffusion and mixing in fluid flow (with P. Constantin, A. Kiselev, and L. Ryzhik),
Ann. of Math. 168 (2008), 643-674.
- Pulsating front speed-up and quenching of reaction by fast advection,
Nonlinearity 20 (2007), 2907-2921.
- KPP pulsating front speed-up by flows (with L. Ryzhik),
Comm. Math. Sci. 5 (2007), 575-593.
- Coefficients of orthogonal polynomials on the unit circle and higher order Szegö theorems (with L. Golinskii),
Constr. Approx. 26 (2007), 361-382.
- Sharp transition between extinction and propagation of reaction,
J. Amer. Math. Soc. 19 (2006), 251-263.
- Quenching of combustion by shear flows (with A. Kiselev),
Duke Math. J. 132 (2006), 49-72.
- On discrete models of the Euler equation (with A. Kiselev),
Int. Math. Res. Notices 2005, 2315-2339.
- Quenching and propagation of combustion without ignition temperature cutoff,
Nonlinearity 18 (2005), 1463-1475.
- Sum rules for Jacobi matrices and divergent Lieb-Thirring sums,
J. Funct. Anal. 225 (2005), 371-382.
- Higher order Szegö theorems with two singular points (with B. Simon),
J. Approx. Theory 134 (2005), 114-129.
- Sparse potentials with fractional Hausdorff dimension,
J. Funct. Anal. 207 (2004), 216-252.
- Sum rules and the Szegö condition for orthogonal polynomials on the real line (with B. Simon),
Comm. Math. Phys. 242 (2003), 393-423.
- The Szegö condition for Coulomb Jacobi matrices,
J. Approx. Theory 121 (2003), 119-142.
- Note on regular embeddings of complete bipartite graphs (with R. Nedela and M. koviera),
Discrete Math. 258 (2002), 379-381.
- Bipartite maps, Petrie duality and exponent groups (with R. Nedela and M. koviera),
Atti Sem. Mat. Fis. Univ. Modena 49 (2001), 109-133.
- The diameter of lifted digraphs,
Australas. J. Combin. 19 (1999), 73-82.
- Construction of regular maps with multiple edges,
International Scientific Conference on Mathematics. Proceedings, 155-160, Univ. ilina, 1998.
Research supported in part by the NSF and Alfred P. Sloan Foundation