Research interests
Primary: Partial Differential Equations (Dispersive Equations and Wave Equations: asymptotic behavior and well-posedness issues).
Secondary: Harmonic Analysis, Optimization.
Classification Of Radial Solutions Of Energy-Critical Wave Systems (with T. Duyckaerts), preprint.
The Blow-up Rate For A Loglog Non-scaling Invariant Semilinear Wave Equation (with H. Zaag), to appear in Nonlinear Differential Equations and Applications.
Global Dynamics Above The Ground State Energy For The Energy-Critical Klein-Gordon Equation, Transactions Of The American Mathematical Society Volume 377, Number 10, October 2024, Pages 6883–6935.
Global Existence Of Solutions Of A Loglog Energy-Supercritical Klein-Gordon Equation, Journal of Dynamics and Differential Equations (2022), https://doi.org/10.1007/s10884-021-10119-w
Local Well-Posedness And Parabolic Smoothing Of Solutions Of Fully Nonlinear Third-Order Equations On The Torus , Nonlinear Anal. 221 (2022), Paper No. 112845, 45 pp.
Scattering Above Energy Norm Of Solutions Of A Focusing Size-Dependent Log Energy-Supercritical Schrodinger Equation With Radial Data Below Ground State , J. Evol. Equ. 22 (2022), no. 2, Paper No. 36, 28 pp.
On Jensen-type Inequalities For Nonsmooth Radial Scattering Solutions Of A Loglog Energy-supercritical Schrodinger Equation, International Mathematics Research Notices, Volume 2020, Issue 8, April 2020, 2501–2541.
A Weak Form Of The Soliton Resolution Conjecture For High-Dimensional Fourth-Order Schrodinger Equations , Journal of Hyperbolic Differential Equations, Vol. 14, No. 2 (2017) 249-300.
Blow-up Of The Critical Sobolev Norm For Nonscattering Radial Solutions Of Supercritical Wave Equations In Space Dimension 3 (with Thomas Duyckaerts), Bulletin de la SMF 145, fascicule 3 (2017), 507-573.
Global Dynamics Above The Ground State For The Energy-critical Schrodinger Equation With Radial Data (with Kenji Nakanishi), Communications On Pure and Applied Analysis, Volume 15, Issue 6, November 2016, Pages: 2023-2058.
On The Interpolation With The Potential Bound For Global Solutions Of The Defocusing Cubic Wave Equation on T2 , Journal Of Functional Analysis, Volume 270, Issue 9, May 2016, Pages 3280-3306.
Scattering Of Rough Solutions Of The Nonlinear Klein-Gordon Equations In 3D (with Soonsik Kwon), Adv. Differential Equations Volume 21, Number 3/4 (2016), 333-372.
On Control Of Sobolev Norms For Some Semilinear Wave Equations With Localized Data , Journal Of Functional Analysis, Volume 265, Issue 11, December 2013, Pages 2724-2752 (summary in RIMS Kokyuroku Bessatsu B42, August 2013).
Global Well-Posedness Of The Maxwell-Klein-Gordon Equation Below The Energy Norm (with Markus Keel, Terence Tao), Disc. Cont. Dynam. Systems A.,30 (2011), no. 3, 573-621.
Bootstrapped Morawetz Estimates And Resonant Decomposition For Low Regularity Global Solutions Of Cubic NLS On R2 (with Jim Colliander), Communications On Pure And Applied Analysis, 10 (2011), no. 2, 397-414.
Introduction To Scattering For Radial 3D NLKG Below Energy Norm , J. Differential Equations (2010), no. 4, 893-923.
Global Analysis Of The Defocusing Cubic Wave Equation In Dimension 3 , Ph.D thesis (advisor: Terence Tao), LAP LAMBERT Academic Publishing (November 6, 2013).
Adapted Linear-Nonlinear Decomposition And Global Well-posedness For Solutions To The Defocusing Cubic Wave Equation On R3 , Disc. Cont. Dynam. Systems A,Vol 24, Number 4, 2009, 1307-1323.
Global Well-posedness For The Radial Defocusing Cubic Wave Equation on R3 And For Rough Data , EJDE, 166, 2007, 1-22.
Bilinear Local Smoothing Estimate For Airy Equation (with S. Kwon), Differential and Integral Equations, 25 (2012), No.1-2, 75-83.
A Remark On Barely Hsp Supercritical Wave Equations , Analysis And PDE 5-1 (2012), 199-218.
Scattering Above Energy Norm Of Solutions Of A Loglog Energy-Supercritical Schrodinger equation With Radial Data , Journal Of Differential Equation, 250 (2011), no. 1, 292-319. Corrigendum, 264 (2018), no. 9, 6013-6024.
Global Existence Of Smooth Solutions Of A 3D Loglog Energy-supercritical Wave Equation , Analysis and PDE, Vol 2, Num 3, 261-280, 2009.
Segmentation Of A Vector Field: Dominant Parameter And Shape Optimization (with G. Aubert, M. Barlaud, E. Debreuve), J. Math Imaging Vis, 2006, vol 24, num 2, pp 259-276.