Publications
My research is supported by the National Science Foundation. Pdf files of some recent publications are available here:
- Nonlinear variational surface waves, Submitted to Communications in Information and Systems, (with L. Austria)
- Long time solutions for a Burgers-Hilbert equation via a modified energy method, Proceedings of the AMS, In Press, 2013 (with M. Ifrim, D. Tataru, and T. K. Wong)
- Self-similar solutions for the diffraction of a weak shocks, J. Computational Science, 4 (2013), 92-100 (with A. M. Tesdall)
- A quasi-linear Schrodinger equation for large amplitude inertial oscillations in a rotating shallow fluid, IMA Journal of Applied Mathematics, May, 2013 (with M. Ifrim)
- Enhanced lifespan of smooth solutions of a Burgers-Hilbert equation, SIAM J. Math. Anal., 44 (2012), 2039-2052 (with M. Ifrim)
- On the self-similar diffraction of a weak shock into an expansion wavefront, SIAM J. Appl. Math., 72 (2012), 124-143 (with A. M. Tesdall)
- Nonlinear hyperbolic surface waves, in IMA Volume on Nonlinear Conservation Laws and Applications (2011), 303-314
- On the weakly nonlinear Kelvin-Helmholtz instability of tangential discontinuities in MHD, J. Hyperbolic Differential Equations, 8 (2011), 691-726 (with J. Thoo)
- Nonlinear Hamiltonian waves with constant frequency and surface waves on vorticity discontinuity, Comm. Pure Appl. Math., 63 (2010) 303-336 (with J. Biello)
- Orientation waves in a director field with rotational inertia, Kinetic and Related Models 2 (2009), 1-37 (with G. Ali)
- Diffractive nonlinear geometrical optics for variational wave equations and the Einstein equations, Comm. Pure Appl. Math. 60 (2007), 1522-1557 (with G. Ali)
- Short time existence of nonlinear Hamiltonian waves, J. Hyperbolic Differential Equations 3 (2006), 247-267
- Weak shock reflection in A Celebration of Mathematical Modeling, 93-112, Kluwer, Dordrecht, 2004 (with A. M. Tesdall)
- Nonlinear surface waves on a tangential discontinuity in magnetohydrodynamics , Quart. Appl. Math. 61 (2003), 451-474 (with G. Ali)
- Singularity formation and instability in the unsteady inviscid and viscous Prandtl equations, Communications in Mathematical Sciences 1 (2003) (with L. Hong)
- Transonic solutions for the Mach reflection of weak shocks, in Proceedings of the Symposium Transsonicum IV, ed. H. Sobieckzy, 7-12, Kluwer, 2003 (with A. Tesdall)
- Nonlinear hyperbolic wave propagation in a one-dimensional random medium, Wave Motion, 37 (2003), 381-405 (with J. Thoo)
- Hamiltonian equations for scale-invariant waves, Stud. Appl. Math. 108 (2002) 305-321 (with G. Ali, and D. F. Parker)
- Self-similar solutions for weak shock reflection, SIAM J. Appl. Math. 63 (2002), 42-61 (with A. Tesdall)
- Reactive autophobic spreading of drops, J. Comp. Phys. 182 (2002), 1-32 (with Z. Li, and H. Zhao)
A full publication list is in my CV.