Reaction-Diffusion Equations, Homogenization, and Probability

Fluid Dynamics and Active Scalars

Drift-Diffusion Equations, Mixing, and Chemotaxis

Spectral Theory, Orthogonal Polynomials, Graph Theory, etc.

- Homogenization for space-time-dependent KPP reaction-diffusion equations and G-equations (with Y.P. Zhang),
*preprint*.

- Virtual linearity for KPP reaction-diffusion equations,
*preprint*.

- Quantitative homogenization for combustion in random media (with Y.P. Zhang),
*Ann. Inst. H. Poincaré Anal. Non Linéaire*, to appear.

- Optimal estimates on the propagation of reactions with fractional diffusion (with Y.P. Zhang),
*Arch. Ration. Mech. Anal.***247**(2023), Article 93, 33pp.

- Subadditive theorems in time-dependent environments (with Y.P. Zhang),
*Electron. J. Probab.***28**(2023), 1-23.

- Homogenization for time-periodic KPP reactions,
*Nonlinearity***36**(2023), 1918-1927.

- Long time dynamics for combustion in random media (with Y.P. Zhang),
*Arch. Ration. Mech. Anal.***243**(2022), 33-94.

- Stochastic homogenization for reaction-diffusion equations (with J. Lin),
*Arch. Ration. Mech. Anal.***232**(2019), 813-871.

- Multidimensional transition fronts for Fisher-KPP reactions (with A. Alwan, Z. Han, J. Lin, and Z. Tao),
*Nonlinearity***32**(2019), 927-941.

- 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.

- Transition fronts for inhomogeneous Fisher-KPP reactions and non-local diffusion (with T.S. Lim),
*Trans. Amer. Math. Soc.***368**(2016), 8615-8631.

- Transition fronts for inhomogeneous monostable reaction-diffusion equations via linearization at zero (with T. Tao and B. Zhu),
*Nonlinearity***27**(2014), 2409-2416.

- 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.

- Reaction-diffusion front speed enhancement by flows,
*Ann. Inst. H. Poincaré Anal. Non Linéaire***28**(2011), 711-726.

- Sharp asymptotics for KPP pulsating front speed-up and diffusion enhancement by flows,
*Arch. Ration. Mech. Anal.***195**(2010), 441-453.

- 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.

- 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.

- Quenching and propagation of combustion without ignition temperature cutoff,
*Nonlinearity***18**(2005), 1463-1475.

- Local regularity and finite time singularity for the generalized SQG equation on the half-plane,
*preprint*.

- An improved regularity criterion and absence of splash-like singularities for g-SQG patches (with J. Jeon),
*Anal. PDE*, to appear.

- Uniqueness of positive vorticity solutions to the 2D Euler equations on singular domains (with Z. Han),
*Arch. Ration. Mech. Anal.***247**(2023), Article 84, 22pp.

- Euler equations on general planar domains (with Z. Han),
*Ann. PDE***7**(2021), Article 20, 31pp.

- The Euler equations in planar domains with corners (with C. Lacave),
*Arch. Ration. Mech. Anal.***234**(2019), 57-79.

- 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), 1253–1315.

- Finite time singularity for the modified SQG patch equation (with A. Kiselev, L. Ryzhik, and Y. Yao),
*Ann. of Math. (2)***184**(2016), 909-948.

- Blow up for the 2D Euler equation on some bounded domains (with A. Kiselev),
*J. Differential Equations***259**(2015), 3490-3494.

- A note on stability shifting for the Muskat problem (with D. Córdoba and J. Gómez-Serrano),
*Philos. Trans. A***373**(2015), 20140278.

- Exponential growth of the vorticity gradient for the Euler equation on the torus,
*Adv. Math.***268**(2015), 396-403.

- On discrete models of the Euler equation (with A. Kiselev),
*Int. Math. Res. Notices***2005**, 2315-2339.

- Numerical evidence of exponential mixing by alternating shear flows (with L.-T. Cheng, F. Rajasekaran, and K.Y.J. Wong),
*Comm. Math. Sci.***21**(2023), 529-541.

- On the fast spreading scenario (with S. He and E. Tadmor),
*Comm. Amer. Math. Soc.***2**(2022), 149-171.

- Convection-induced singularity suppression in the Keller-Segel and other non-linear PDEs (with G. Iyer and X. Xu),
*Trans. Amer. Math. Soc.***374**(2021), 6039-6058.

- Universal mixers in all dimensions (with T. Elgindi),
*Adv. Math.***356**(2019), 106807, 33pp.

- Mixing and un-mixing by incompressible flows (with Y. Yao),
*J. Eur. Math. Soc.***19**(2017), 1911-1948.

- 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.

- 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.

- On divergence-free drifts (with G. Seregin, L. Silvestre, and V. Šverák),
*J. Differential Equations***252**(2012), 505-540.

- Exit times of diffusions with incompressible drifts (with G. Iyer, A. Novikov, and L. Ryzhik),
*SIAM J. Math. Anal.***42**(2010), 2484-2498.

- Diffusion in fluid flow: Dissipation enhancement by flows in 2D,
*Comm. Partial Differential Equations***35**(2010), 496-534.

- 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. (2)***168**(2008), 643-674.

- On the high intensity limit of interacting corpora (with P. Constantin),
*Comm. Math. Sci.***8**(2010), 173-186.

- Coefficients of orthogonal polynomials on the unit circle and higher order Szegö theorems (with L. Golinskii),
*Constr. Approx.***26**(2007), 361-382.

- 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. Škoviera),
*Discrete Math.***258**(2002), 379-381.

- Bipartite maps, Petrie duality and exponent groups (with R. Nedela and M. Škoviera),
*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. Žilina,*1998.

Research supported in part by the NSF, Alfred P. Sloan Foundation, and Simons Foundation