The University of North Carolina at Chapel Hill

Most of my preprints / publications are available from the ArXiv.

Research Publications:

• (with T. Rhoads) Long-time existence for systems of quasilinear wave equations. Matematica 2 (2023), 37–84. (arXiv: 2203.08599)
• (with A. Stewart) On a system of weakly null semilinear wave equations. Anal. Math. Phys. 12 (2022), Paper No. 125. (arXiv:2204.06665)
• (with K. Hepditch) A local energy estimate for 2-dimensional Dirichlet wave equations. Involve 16 (2023), 483–492. (.pdf)
• (with M. Facci) Global existence for quasilinear wave equations satisfying the null condition. Houston J. Math. 48 (2022), 631–653. (arXiv:2208.12659)
• (with M. Facci and A. Mcentarffer) An r^p-weighted local energy approach to global existence for null form semilinear wave equations. Involve 17 (2024), 1–9. (.pdf)
  
• (with K. Datchev, J. Shapiro, and M. Tohaneanu)  On the interaction of metric trapping and a boundary.  Proc. Amer. Math. Soc. 149 (2021), 3801–3812.  (arXiv: 2008.05408)
• (with J. Marzuola and D. Tataru)  Quasilinear Schrödinger equations III: Large data and short time.  Arch. Ration. Mech. Anal. 242 (2021), 1119–1175.  (arXiv: 2001.01014)
• (with K. Morgan) Global existence for systems of quasilinear wave equations in (1+4)-dimensions. J. Differential Equations 268 (2020), 2309–2331. (arXiv:1812.11956)
• (with R. Booth, H. Christianson, and J. Perry) Localized energy for wave equations with degenerate trapping. Math. Res. Lett. 26 (2019), 991–1025. (arXiv:1712.05853)
• (with J. Sterbenz and D. Tataru) Local energy decay for scalar fields on time dependent non-trapping backgrounds. Amer. J. Math. 142 (2020), 821–883. (arXiv: 1703.08064)
• (with D. Spencer) Global existence for a coupled wave system related to the Strauss conjecture. Comm. Pure Appl. Anal. 17 (2018), 593–604. (arXiv: 1701.05642)
• (with C. Wang) The Strauss conjecture on asymptotically flat space-times. SIAM J. Math. Anal. 49 (2017), 4579–4594. (arXiv: 1605.02157)
• (with D. Tataru and M. Tohaneanu) Pointwise decay for the Maxwell field on black hole space-times. Adv. Math. 316 (2017), 53–93. (arXiv: 1411.3693)
• (with J. Helms) Almost global existence for 4-dimensional quasilinear wave equations in exterior domains. Differential Integral Equations 27 (2014), 837–878. (arXiv: 1402.4873)
• (with P. Laul, S. Tikare, and M. Tohaneanu) Localized energy estimates on Myers-Perry space-times. SIAM J. Math. Anal. 47 (2015), 1933–1957. (arXiv: 1401.0465)
• (with H. Lindblad, C.D. Sogge, M. Tohaneanu, and C. Wang) The Strauss conjecture on Kerr black hole backgrounds. Math. Ann. 359 (2014), 637–661. (arXiv: 1304.4145)
• (with H. Christianson) Sharp local smoothing for manifolds with smooth inflection transmission. Indiana Univ. Math. J. 63 (2014), 969–992. (arXiv: 1303.3309)
• (with J. Marzuola and D. Tataru)  Quasilinear Schrödinger equations II: Small data and cubic nonlinearities.  Kyoto J. Math. 54 (2014), 529–546.  (arXiv: 1208.0544)
• (with J. Helms) The lifespan for 3-dimensional quasilinear wave equations in exterior domains.  Forum Math. 26 (2014), 1883–1918.  (arXiv: 1204.4689)
• (with H. Christianson, J. Marzuola, and M. Taylor) Nonlinear bound states on weakly homogeneous spaces.  Comm. Partial Differential Equations 39 (2014), 34–97.  (arXiv: 1203.3612)
• (with J. Marzuola and D. Tataru)  Quasilinear Schrödinger equations I: Small data and quadratic interactions.  Adv. Math. 231 (2012), 1151–1172.  (arXiv: 1106.0490)
• (with D. Tataru and M. Tohaneanu)  Price’s law on nonstationary spacetimes.  Adv. Math. 230 (2012), 995–1028.  (arXiv: 1104.5437)
• (with M. Taylor)  Dispersive wave estimates on 3D hyperbolic space.  Proc. Amer. Math. Soc. 140 (2012), 3861–3866.
• (with J. Perry)  Global solutions to quasilinear wave equations in homogeneous waveguides with Neumann boundary conditions.  Commun. Pure Appl. Anal. 11 (2012), 547–556.
• (with P. Laul)  Localized energy estimates for wave equations on high dimensional Schwarzschild space-times.  Proc. Amer. Math. Soc.  140 (2012), 3247–3262.  (arXiv: 1008.4626)
• (with C.D. Sogge)  Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles.  Discrete Contin. Dyn. Sys. 28 (2010), 1589–1601.  (arXiv: 0910.0433)
• (with M. Taylor)  Nonlinear waves on 3D hyperbolic space.  Trans. Amer. Math. Soc. 363 (2011), 3489–3529.
• (with D. Tataru)  Decay estimates for variable coefficient wave equations in exterior domains.  Advances in Phase Space Analysis of Partial Differential Equations, In Honor of Ferruccio Colombini’s 60th Birthday.  Progress in Nonlinear Differential Equations and Their Applications, Vol. 78, 2009.  p. 201–217.  (arXiv: 0806.3409)
• (with K. Hidano, H. Smith, C. D. Sogge, and Y. Zhou)  On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles.  Trans. Amer. Math. Soc. 362 (2010), 2789–2809.  (arXiv: 0805.1673)
• (with J. Marzuola, D. Tataru, and M. Tohaneanu)  Strichartz estimates on Schwarzschild black hole backgrounds.  Comm. Math. Phys. 293 (2010), 37–83.  (arXiv: 0802.3942)
• (with Y. Du, C.D. Sogge, and Y. Zhou)  Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions. Comm. Partial Differential Equations 33 (2008), 1487–1506.  (arXiv: 0710.2026)
• (with D. Tataru)  Global parametrices and dispersive estimates for variable coefficient wave equations.  Math. Ann. 353 (2012), 1183–1237.  (arXiv: 0707.1191)
• (with J. Marzuola and D. Tataru)  Strichartz estimates and local smoothing estimates for asymptotically flat Schrödinger equations. J. Funct. Anal. 255 (2008), 1497–1553.  (arXiv: 0706.0544)
• (with J. Marzuola and D. Tataru)  Wave packet parametrices for evolutions governed by PDO’s with rough symbols. Proc. Amer. Math. Soc. 136 (2008), 597–604.   (arXiv: math/0611252)
• (with M. Nakamura) General quasilinear wave equations with localized dissipation in exterior domains.  J. Differential Equations  233 (2007), 313–344. 
• (with B. Thomases)  Elastic waves in exterior domains, Part II: Global existence with a null structure.  Int. Math. Res. Not. 2007, 1–43.   (arXiv: math/0605110)
• Elastic waves in exterior domains, Part I: Almost global existence.  Int. Math. Res. Not.  2006, 1–41.
• (with C.D. Sogge)  Global existence of null-form wave equations in exterior domains.  Math. Z.  256 (2007), 521–549.   (arXiv: math/0611489)
• (with A. Stewart)  Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions.   Trans. Amer. Math. Soc. 360 (2008), 171–188. (arXiv: math/0509326)
• (with C.D. Sogge) Long time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods.  SIAM J. Math. Anal. 38 (2006), 188–209. 
• (with M. Lacey)  Paraproducts in one and several parameters.  Forum Math. 19 (2007), 325–351.   (arXiv: math/0502334)
• (with M. Nakamura and C.D. Sogge)  Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition.  Japan. J. Math. 31 (2005), 391–472.  (arXiv: math/0409363)
• (with C. D. Sogge and A. Stewart) Nonlinear hyperbolic equations in infinite homogeneous waveguides.  Comm. Partial Differential Equations 30 (2005), 643–661.   (arXiv: math/0411513)
• (with C. D. Sogge) Global existence for Dirichlet-wave equations with quadratic nonlinearities in high dimensions.   Math. Ann. 336 (2006), 391–420.   (arXiv: math/0404420)
• (with M. Nakamura and C. D. Sogge) Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains.  Forum Math. 17 (2005), 133–168.    (arXiv: math/0409362)
• (with C. D. Sogge) Hyperbolic trapped rays and global existence of quasilinear wave equations. Invent. Math. 159 (2005), 75–117.   (arXiv: math/0301290)
• Global existence for semilinear wave equations exterior to nontrapping obstacles.  Houston J. Math.  30 (2004), 259–281.  (arXiv: math/0210246)
• Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle.  Trans. Amer. Math. Soc. 356 (2004), 4839–4855.   (arXiv: math/0210227)

 

Extended Abstracts:

• Local energy decay for the wave equation. Notices Amer. Math. Soc. 63 (2016), 1158-1159.
  
• Low regularity local well-posedness for quasilinear Schrödinger equations. Oberwolfach Reports 41 (2013), 2352-2354. (.pdf)
  
• Long time existence for nonlinear wave equations in exterior domains.  Oberwolfach Reports 41 (2010), 59–62.  (.pdf)
  
• Strichartz estimates on Schwarzschild space-times.  Oberwolfach Reports 44 (2007),  8–11.   (.pdf)
  

 

Feature in Carolina Scientific, Fall 2016