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Robert Pego, Professor Ph.D., University of California, Berkeley Email: rpego AT cmu DOT edu Office: Wean Hall 6127 Phone: 4122682553 Personal web siteResearch: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 selfsimilar structures in kinetic models of coagulation has established some remarkable rigorous connections to random shock dynamics (Burgers turbulence model), LevyKhintchine 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 NavierStokes 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 highperforming numerical schemes were proposed based on it.
Ongoing investigations involve coagulationfragmentation models of telomeric DNA and animal groups, and BoseEinstein condensation in a model equation arising in kinetic theory for Compton scattering of photons.
Selected Publications:  G. Menon and R. L. Pego, The scaling attractor and ultimate dynamics in Smoluchowski's coagulation equations, J. Nonl. Sci. 18 (2008) 143190.

J.G. Liu, J. Liu and R. L. Pego, Stability and convergence of efficient NavierStokes solvers via a commutator estimate, Comm. Pure Appl. Math. 60 (2007) 14431487.

G. Menon and R. L. Pego, Approach to selfsimilarity in Smoluchowski's coagulation equations, Comm. Pure Appl. Math. 57 (9) (2004) 11971232.

G. Friesecke and R. L. Pego, Solitary waves on FermiPastaUlam lattices IV: Proof of stability at low energy, Nonlinearity 17 (2004) 229251.

R. L. Pego and J. R. Quintero, A host of travelingwave solutions for a model of threedimensional waterwave dynamics, J. Nonl. Sci. 12 (2002) 5983.

B. Niethammer and R. L. Pego, Nonselfsimilar behavior in the LSW theory of Ostwald ripening, J. Stat. Phys. 95 (1999) 867902.
Recent CNA Publications:  18CNA001, Existence of solitary waves in one dimensional peridynamics, Robert L. Pego, TruongSon Van, (download paper)
 16CNA025, Coagulation And Universal Scaling Limits For Critical GaltonWatson Processes
, Gautam Iyer, Nicholas Leger, Robert L. Pego, (download paper)
 16CNA020, Cutoff Estimates For The BeckerDöring Equations
, Ryan Murray, Robert L. Pego, (download paper)
 16CNA004, Least Action Principles For Incompressible Flows And Optimal Transport Between Shapes, JianGuo Liu, Robert L. Pego, Dejan Slepčev, (download paper)
 15CNA023, BoseEinstein condensation in a hyperbolic model for the Kompaneets equation, Joshua Ballew, Gautam Iyer, Robert L. Pego, (download paper)
 15CNA022, Global dynamics of BoseEinstein condensation for a model of the Kompaneets equation, C. David Levermore, Hailiang Liu, Robert L. Pego, (download paper)
 15CNA018, Polynomial Decay to Equilibrium for the BeckerDöring Equations, Ryan Murray, Robert L. Pego, (download paper)
 15CNA017, CoagulationFragmentation Model for Animal GroupSize Statistics, Pierre Degond, JianGuo Liu, Robert L. Pego, (download paper)
 14CNA001, On generating functions of Hausdorff moment sequences, JianGuo Liu, Robert L. Pego, (download paper)
 13CNA017, Global existence for two extended NavierStokes systems, Mihaela Ignatova, Gautam Iyer, James P. Kelliher, Robert L. Pego, Arghir Zarnescu, (download paper)
