Robert Pego

Robert Pego

Emeritus Professor
Department of Mathematical Sciences
Carnegie Mellon University

Office: Wean Hall 6127
Phone: 412-268-2553
Fax: 412-268-6380
E-mail: rpego at cmu.edu

Research interests include:

Dynamics in infinite-dimensional physical systems, universal scaling behavior in models of clustering and coarsening, stability of nonlinear waves, numerical methods for incompressible viscous flow.

Former Ph.D. students

List of articles on MathSciNet (subscription)

Recent publications:

(with Jian-Guo Liu) Rigidly breaking potential flows and a countable Alexandrov theorem for polytopes, arXiv:2411.05606

(with Sangmin Park) Convergence and non-convergence in a nonlocal gradient flow, arXiv:2308.04281

(with Jian-Guo Liu) A simple construction of fat Cantor sets, Amer. Math. Monthly 131(6) (2024) 525

(with Benjamin Ingimarson) Existence of solitary waves in particle lattices with power-law forces, Nonlinearity 37 (2024) 125016, arXiv:2406.09184

(with Benjamin Ingimarson) On long waves and solitons in particle lattices with forces of infinite range, SIAM J. Appl. Math 84 (2024) 808-830, arXiv:2310.02271

(with J. Ballew, G. Iyer, C. D. Levermore and H. Liu) Global dynamics and photon loss in the Kompaneets equation, SIAM J. Math. Anal. 55 (2023) 5715-5750, arXiv:2208.09755

(with B. Guelmame, S. Junca and D. Clamond) Global weak solutions of a Hamiltonian regularized Burgers equation, J. Dyn. Diff Eqns. (2022) online, hal-02478872

(with Jian-Guo Liu) In search of local singularities in ideal potential flows with free surface, arXiv:2108.00445

(with Won Eui Hong) Exclusion and multiplicity for stable communities in Lotka-Volterra systems, J. Math. Biol. (2021) 83:16, 21-CNA-001, arXiv:2102.00611

(with B. Niethammer, A. Schlicting and J. J. L. Velázquez) Oscillations in a Becker-Doering model with injection and depletion, SIAM J. Appl. Math. 82 (2022) 1194-1219, arXiv:2102.06751

(with Juan J. L. Velázquez) Temporal oscillations in Becker-Doering equations with atomization, Nonlinearity 33 (2020) 1812-1846, arXiv:1905.02605

(with Jian-Guo Liu and Barbara Niethammer) Self-similar spreading in a merging-splitting model of animal group size, J. Stat. Phys. (2019) online, arXiv:1903:10020

(with Yue Pu and Jian-Guo Liu) Well-posedness and derivative blow-up for a dispersionless regularized shallow water system, Nonlinearity 32 (2019) 4346-4376, arXiv:1810:06096

(with Yue Pu, Didier Clamond, and Denys Dutykh) Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations, Comm. Math. Sci. 16 (2018) 1361-1378, arXiv:1805:06842

(with Truong-Son Van) Existence of solitary waves in one dimensional peridynamics, J. Elasticity 136 (2019) 207-236, 18-CNA-001, arXiv:1802.00516

(with Jian-Guo Liu and Dejan Slepcev) Least action principles for incompressible flows and geodesics between shapes, Calc. Var. 58 (2019) 179 (read online), 16-CNA-004, arXiv:1604.03387

(with G. Iyer and N. Leger) Coagulation and universal scaling limits for critical Galton-Watson processes, Adv. Appl. Prob. 50 (2018) 504-542, 16-CNA-025, arXiv:1610:04647

(with Ryan Murray) Cutoff estimates for the Becker-Döring equations, Commun. Math. Sci. 15 (2017) 1685-1702, 16-CNA-020, arXiv:1609:07965

(with Ryan Murray) Algebraic decay to equilibrium for the Becker-Döring equations, SIAM J. Math. Anal. 48 (2016) 2819-42, 15-CNA-018, arXiv:1509:01762

(with Pierre Degond and Jian-Guo Liu) Coagulation-fragmentation model for animal group-size statistics, J. Nonl. Sci. 27 (2017) 379-424, 15-CNA-017, arXiv:1510:06077

(with Jian-Guo Liu) On generating functions of Hausdorff moment sequences, Trans. Amer. Math. Soc. 368 (2016) 8499-8518, 14-CNA-001, arXiv:1401.8052

(with J. Ballew and G. Iyer) Bose-Einstein condensation in a hyperbolic model for the Kompaneets equation, SIAM J. Math. Anal. 48 (2016) 3840-59, 15-CNA-023, arXiv:1512:06950

(with C. David Levermore and Hailiang Liu) Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation, SIAM J. Math. Anal. 48 (2016) 2454-94,

(with Shu-Ming Sun) Asymptotic linear stability of solitary water waves, Arch. Rational. Mech. Anal. 222 (2016) 1161-1216, 10-CNA-15, arXiv:1009.0494

(with M. Ignatova, G. Iyer, J.P. Kelliher and A. Zarnescu) Global existence for two extended Navier-Stokes systems, Comm. Math. Sci. 13 (2015) 249-267, 13-CNA-017, arXiv:1308.4735

(with G. Iyer and N. Leger) Limit theorems for Smoluchowski dynamics associated with critical continuous-state branching processes, Ann. Appl. Prob. 25 (2015) 675-713, 13-CNA-002, pdf

(with G. Iyer and A. Zarnescu) Coercivity and stability results for an extended Navier-Stokes system, J. Math. Phys. 53 (2012) 115605, 12-CNA-003, arXiv:1202.5761

(with T. Mizumachi and José Raúl Quintero) Asymptotic stability of solitary waves in the Benney-Luke model of water waves, Diff. Int. Eq. 26 (2013) 253-301, 12-CNA-002, arXiv:1202.0450

(with J.-G. Liu and J. Liu) Stable and accurate pressure approximation for unsteady incompressible viscous flow, J. Comp. Phys. 229 (2010) 3428-3453. preprint

(with E. Cozzi) On optimal estimates for the Laplace-Leray commutator in planar domains with corners, Proc. Amer. Math. Soc. 139 (2011) 1691-1706. preprint

(with R. Kollár) Spectral stability of vortices in two-dimensional Bose-Einstein condensates via the Evans function and Krein signature, Appl. Math. Res. Express 2012 (2012) 1-46 09-CNA-17

Minicourse lectures for PASI2009 (Mexico City): Dynamics and scaling in models of coarsening and coagulation

(with S. Dai and B. Niethammer) Crossover in coarsening rates for the monopole approximation of the Mullins-Sekerka model with kinetic drag, Proc. Roy. Soc. Edin. A 140 (2010) 553-571. 09-CNA-003

(with G. Menon and B. Niethammer) Dynamics and self-similarity in min-driven clustering, Trans. Amer. Math. Soc. 362 (2010) 6591-6618. 08-CNA-013

(with J.-G. Liu) Stable discretization of magnetohydrodynamics in bounded domains, Comm. Math. Sci. 8 (2010) 234-251, 08-CNA-018

(with J.-G. Liu and J. Liu) Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions, Chinese Annals Math. B 30 (2009) 743-768. preprint

(with Tetsu Mizumachi) Asymptotic stability of Toda lattice solitons, Nonlinearity 21 (2008) 2099-2111. 07-CNA-008

(with Govind Menon) The scaling attractor and ultimate dynamics in Smoluchowski's coagulation equations, J. Nonl. Sci. 18 (2008) 143-190. 06-CNA-008

(with Govind Menon) Universality classes in Burgers turbulence, Comm. Math. Phys. 273 (2007) 177-202. 06-CNA-006

(with Govind Menon) Dynamical scaling in Smoluchowski's coagulation equations: uniform convergence. SIAM Review 48 (2006) no. 4, 745--768 pdf

(with J.-G. Liu and J. Liu) Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Comm. Pure Appl Math. 60 (2007) 1443--1487. preprint

Lectures on dynamics in models of coarsening and coagulation, in Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization (Lec. Notes Ser. Inst. Math. Sci., Nat. Univ. Singapore). Eds. Weizhu Bao and Jian-Guo Liu, World Scientific (Singapore) 2007. 06-CNA-001

(with G. Schneider and H. Uecker) Long-time persistence of Korteweg-de Vries solitons as transient dynamics in a model of inclined film flow, Proc. Roy. Soc. Edinburgh 137 (2007) 133-146.