Department of Mathematical Sciences
Colloquia and Seminars
Areas of Research
About the Department
Ph.D., University of California, BerkeleyE-mail:
rpego AT cmu DOT eduOffice:
Wean Hall 6130Phone:
412-268-2553Personal web site
My research concerns nonlinear dynamics in PDE, especially coherent structures and nonlinear waves. One focus is to explain the emergence of `universal' behavior in models of complex systems. Recent work on self-similar structures in kinetic models of coagulation has established some remarkable rigorous connections to random shock dynamics (Burgers turbulence model), Levy-Khintchine formulae, and the classic theory of branching processes in probability theory.
Work on solitary waves has achieved proofs of linear stability for the full Euler equations of water waves without surface tension, and nonlinear asymptotic stability for a prototypical model with the same infinitely indefinite variational structure.
Another line of research concerns how to pose correct boundary conditions for the pressure in the Navier-Stokes equations for viscous, incompressible flow with no slip on the boundary. A new theory was developed proving that a particular commutator formula provides a correct and stable pressure, and new high-performing numerical schemes were proposed based on it.
Ongoing investigations involve coagulation-fragmentation models of telomeric DNA and animal groups, and Bose-Einstein condensation in a model equation arising in kinetic theory for Compton scattering of photons.
G. Menon and R. L. Pego, The scaling attractor and ultimate dynamics in Smoluchowski's coagulation equations, J. Nonl. Sci. 18 (2008) 143-190.
J.-G. Liu, J. Liu and R. L. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Comm. Pure Appl. Math. 60 (2007) 1443-1487.
G. Menon and R. L. Pego, Approach to self-similarity in Smoluchowski's coagulation equations, Comm. Pure Appl. Math. 57 (9) (2004) 1197--1232.
G. Friesecke and R. L. Pego, Solitary waves on Fermi-Pasta-Ulam lattices IV: Proof of stability at low energy, Nonlinearity 17 (2004) 229--251.
R. L. Pego and J. R. Quintero, A host of traveling-wave solutions for a model of three-dimensional water-wave dynamics, J. Nonl. Sci. 12 (2002) 59--83.
B. Niethammer and R. L. Pego, Non-self-similar behavior in the LSW theory of Ostwald ripening, J. Stat. Phys. 95 (1999) 867--902.
Recent CNA Publications:
- 13-CNA-017, Global existence for two extended Navier-Stokes systems , Mihaela Ignatova , Gautam Iyer, James P. Kelliher , Robert L. Pego, Arghir Zarnescu, (download paper)
- 13-CNA-002, Limit Theorems for Smoluchowski Dynamics Associated with Critical Continuous-State Branching Processes , Gautam Iyer, Nicholas Leger, Robert L. Pego, (download paper)
- 12-CNA-003, Coercivity and Stability Results for an Extended Navier-Stokes System , Gautam Iyer, Robert L. Pego, Arghir Zarnescu, (download paper)
- 12-CNA-002, Asymptotic stability of solitary waves in the Benney-Luke model of water waves , Tetsu Mizumachi, Robert L. Pego, José Raúl Quintero, (download paper)
- 10-CNA-015, Asymptotic Linear Stability of Solitary Water Waves , Robert L. Pego, Shu-Ming Sun, (download paper)
- 09-CNA-020, On Optimal Estimates for the Laplace-Leray Commutator in Planar Domains with Corners , Elaine Cozzi, Robert L. Pego, (download paper)
- 09-CNA-017, Spectral Stability of Vortices in Two-Dimensional Bose-Einstein Condensates via the Evans Function and Krein Signature , Richard Kollár, Robert L. Pego, (download paper)
- 09-CNA-003, Crossover in coarsening rates for the monopole approximation of the Mullins-Sekerka model with kinetic drag , Shibin Dai, Barbara Niethammer, Robert L. Pego, (download paper)
- 08-CNA-018, Discretization of Magnetohydrodynamics in Bounded Domains , Jian-Guo Liu, Robert L. Pego, (download paper)
- 08-CNA-013, Dynamics and Self-Similarity in Min-Driven Clustering , Govind Menon, Barbara Niethammer, Robert L. Pego, (download paper)