Preprints and Recent Publications

      (with G. Fonseca) The IVP for the Benjamin-Ono equation in weighted Sobolev spaces, J. Funct. Analysis 260, pp. 436-459, 2011.

      .  (with J. Nahas)  On the persistent properties of solutions of nonlinear dispersive equations  in weighted Sobolev spaces, RIMS Kokyuroku Bessatsu (RIMS Proceedings)   pp. 23-36, 2011

      . (with L. Escauriaza, C. E. Kenig,  and L. Vega) Unique Continuation for  Schr\"odinger Evolutions, with applications to profiles of concentration and travelling waves,  Comm.  Math. Phys. 305, pp. 487-512, 2011

       (with F. Linares and G. Fonseca) The IVP for the Benjamin-Ono equation in weighted Sobolev spaces II,   J. Funct. Analysis 262, pp. 2031-2049, 2012

       (with L. Escauriaza, C. E. Kenig,  and L. Vega) Uniqueness Properties of Solutions to  Schr\"odinger Equations,  Bulletin of the AMS 49, pp. 415-442, 2012

       (with C. E. Kenig,  and L. Vega) Lower bounds for non-trivial traveling wave solutions of equations of KdV type,  Nonlinearity 25, pp. 1235--1245, 2012

       (with J. Angulo) The nonlinear Schr\"odinger equation with periodic $\delta$ interaction, Bulletin of the Brazilian Math. Soc. 44, pp. 497--551, 2013

       (with F. Linares and G. Fonseca) The IVP for the dispersion generalized  Benjamin-Ono equation in weighted Sobolev spacesAnnales IHP-Analyse non lineaire 5, pp. 763--790,  2013

        . (with P. Isaza and F. Linares) On decay  properties of solutions of  the k-generalized KdV equation,  Comm.  Math. Phys. 324, pp. 129--146, 2013

        .  (with C. E. Kenig,  and L. Vega) A theorem of Paley-Wiener type for Schrödinger evolutions, Annales Scientifiques  Ec. Norm. Sup. 47, pp. 539--557, 2014

        . 
(with J. Bona, J.-C. Saut and C. Sparber) Dispersive blow up for nonlinear Schr\"odinger equations revisited, Journal Matematiques Pures Appl. 102, pp. 782--811, 2014

        .  (with P. Isaza and F. Linares) Decay  properties for solutions of  fifth order nonlinear dispersive equations, J. Differential Equations, 258, pp. 764--795, 2015
       
        .  (with P. Isaza and F. Linares) On the propagation of regularity and decay of solutions to the k-generalized Korteweg-de Vries equation, Comm. Partial Diff. Eqs. 40, pp. 1336--1364, 2015

        (with F. Linares and G. Fonseca) On persistence properties in fractional weighted spaces,  Proc. of the AMS 143, pp.  5353--5367, 2015
        
        (with L. Escauriaza, C. E. Kenig,  and L. Vega) Hardy Uncertainty Principle, Convexity and Parabolic Evolutions,  Comm. Math. Phys.346, pp. 667-678, 2016

        .  (with P. Isaza and F. Linares) On the propagation of regularities in solutions of the Benjamin-Ono equation,  J. Funct. Analysis 270, pp. 976--1000, 2016

        .  (with P. Isaza and F. Linares) On the propagation of regularities in solutions of the Kadomtsev-Petviashvili equation,  SIAM J. Math. Anal. 48 pp. 1006-1024, 2016

        .  (with F. Linares and D. L. Smith) On the regularity of solutions to a class of nonliear dispersive equations,  to apper in Mathematische Annalen

        . On the IVP for the $k$-Generalized Benjamin-Ono Equation", Harmonic Analysis, Partial Diff.  Eqs., Complex Analysis, Banach spaces, and Operator Theory (Springer) Vol. 1,  349--371, 2016






G. Ponce acknowledges partial support from the National Science Foundation for these works.