ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

Research output

Research output per year 2015 2017 2018 2020 2022 2023

• 36 Article
• 1 Conference contribution
• 1 Chapter (peer-reviewed)

Research output per year

Research output per year

Search results

• 2023

  Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity

  Gubinelli, M., Koch, H. & Oh, T., 28 Jan 2023, (E-pub ahead of print) In: Journal of the European Mathematical Society. 58 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Electric commutators 100%
  • Stochastic Wave Equation 98%
  • Space-time White Noise 96%
  • Random Operators 90%
  • Leverage 88%
• 2022

  Global dynamics for the two-dimensional stochastic nonlinear wave equations

  Gubinelli, M., Koch, H., Oh, T. & Tolomeo, L., 30 Nov 2022, In: International Mathematics Research Notices. 2022, 21, p. 16954–16999 46 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Stochastic Wave Equation 100%
  • Global Dynamics 79%
  • Nonlinear Wave Equation 77%
  • Damped Wave Equation 43%
  • Gibbs Measure 41%

• Three-dimensional stochastic cubic nonlinear wave equation with almost space-time white noise

  Oh, T., Wang, Y. & Zine, Y., 30 Sep 2022, In: Stochastics and Partial Differential Equations: Analysis and Computations. 10, 3, p. 898-963 66 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Space-time White Noise 100%
  • Wave equations 91%
  • Nonlinear Wave Equation 79%
  • White noise 79%
  • Three-dimensional 51%

• Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions

  Gunaratnam, T., Oh, T., Tzvetkov, N. & Weber, H., 9 Jul 2022, In: Probability and Mathematical Physics. 3, 2, p. 343-379 37 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Gaussian Measure 100%
  • Nonlinear Wave Equation 92%
  • Three-dimension 79%
  • Invariant Measure 79%
  • Quasi-invariance 42%

• Probabilistic local well-posedness of the cubic nonlinear wave equation in negative Sobolev spaces

  Oh, T., Pocovnicu, O. & Tzvetkov, N., 7 Jul 2022, In: Annales de l'Institut Fourier. 72, 2, p. 771-830 60 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Local Well-posedness 100%
  • Nonlinear Wave Equation 94%
  • Sobolev Spaces 75%
  • Renormalization 24%
  • Stochastic Partial Differential Equations 23%

• Focusing \Phi^4/3-model with a Hartree-type nonlinearity

  Oh, T., Okamoto, M. & Tolomeo, L., 13 Jun 2022, (Accepted/In press) In: Memoirs of the american mathematical society. 126 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Nonlinearity 100%
  • Gibbs Measure 64%
  • Model 44%
  • Bessel Potential 38%
  • Renormalization 30%

• Optimal integrability threshold for Gibbs measures associated with focusing NLS on the torus

  Oh, T., Sosoe, P. & Tolomeo, L., 31 Mar 2022, In: Inventiones mathematicae. 227, p. 1323–1429 107 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Gibbs Measure 100%
  • Integrability 75%
  • Torus 67%
  • Nonlinear Equations 15%
  • Quintic 10%
• 2021

  Almost conservation laws for stochastic nonlinear Schrödinger equations

  Cheung, K., Li, G. & Oh, T., 30 Jun 2021, In: Journal of Evolution Equations. 21, p. 1865–1894 30 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Stochastic Equations 100%
  • Conservation Laws 90%
  • Nonlinear Equations 77%
  • Cubic equation 47%
  • Globalization 26%

• On global well-posedness of the modified KdV equation in modulation spaces

  Oh, T. & Wang, Y., 30 Jun 2021, In: Discrete and Continuous Dynamical Systems - Series A. 41, 6, p. 2971-2992 22 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Modulation Spaces 100%
  • Global Well-posedness 82%
  • Modified Equations 82%
  • KdV Equation 80%
  • Modulation 57%

• Comparing the stochastic nonlinear wave and heat equations: a case study

  Oh, T. & Okamoto, M., 12 Jan 2021, In: Electronic journal of probability. 26, 9, p. 1-44

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Nonlinear Waves 100%
  • Stochastic Wave Equation 72%
  • Nonlinear Heat Equation 68%
  • Nonlinear Wave Equation 56%
  • Well-posedness 34%
• 2020

  On the stochastic nonlinear Schrödinger equations at critical regularities.

  Oh, T. & Okamoto, M., 31 Dec 2020, In: Stochastics and Partial Differential Equations: Analysis and Computations. 8, p. 869–894 26 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Nonlinear equations 100%
  • Stochastic Equations 96%
  • Nonlinear Equations 74%
  • Regularity 65%
  • Stochastic PDEs 64%

• On the stochastic nonlinear Schrödinger equations with non-smooth additive noise

  Oh, T., Pocovnicu, O. & Wang, Y., Dec 2020, In: Kyoto journal of mathematics. 60, 4, p. 1227-1243 17 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Additive Noise 100%
  • Stochastic Equations 88%
  • Forcing 84%
  • Nonlinear Equations 68%
  • Dispersive Estimates 60%

• Solving the 4NLS with white noise initial data

  Oh, T., Tzvetkov, N. & Wang, Y., 18 Nov 2020, In: Forum of Mathematics, Sigma. 8, 64 p., e48.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • white noise 100%
  • White noise 94%
  • norms 51%
  • contraction 45%
  • nonlinear equations 44%

• Normal form approach to unconditional well-posedness of nonlinear dispersive PDEs on the real line

  Kwon, S., Oh, T. & Yoon, H., 16 Nov 2020, In: Annales de la Faculte des Sciences de Toulouse. 29, 3, p. 649-720

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Real Line 100%
  • Well-posedness 95%
  • Normal Form 95%
  • Modified Equations 89%
  • KdV Equation 88%

• A remark on triviality for the two-dimensional stochastic nonlinear wave equation

  Oh, T., Okamoto, M. & Robert, T., 30 Sep 2020, In: Stochastic processes and their applications. 130, 9, p. 5838-5864 27 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Stochastic Wave Equation 100%
  • Wave equations 89%
  • Damped Wave Equation 87%
  • Nonlinear Wave Equation 77%
  • Limiting Behavior 31%

• Stochastic nonlinear Schrödinger equation with almost space-time white noise

  Forlano, J., Oh, T. & Wang, Y., 31 Aug 2020, In: Journal of the australian mathematical society. 109, 1, p. 44 - 67 24 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Space-time White Noise 100%
  • Stochastic Equations 74%
  • Nonlinear Equations 58%
  • Cubic equation 53%
  • Criticality 17%

• Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations

  Oh, T. & Thomann, L., 24 Jul 2020, In: Annales de la Faculte des Sciences de Toulouse. 29, 1, 21 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Gibbs Measure 100%
  • Nonlinear Wave Equation 92%
  • Invariant Measure 79%
  • Scaling Limit 19%
  • Universality 17%

• Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces

  Oh, T. & Wang, Y., 15 Jun 2020, In: Journal of Differential Equations. 269, 1, p. 612-640 29 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Cubic equation 100%
  • Global Well-posedness 89%
  • Nonlinear equations 87%
  • Modulation Spaces 81%
  • Modified Equations 67%

• Quasi-invariant Gaussian measures for the two-dimensional defocusing cubic nonlinear wave equation

  Oh, T. & Tzvetkov, N., 1 Jun 2020, In: Journal of the European Mathematical Society. 22, 6, p. 1785-1826 42 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Sobolev spaces 100%
  • Wave equations 71%
  • Gaussian Measure 67%
  • Nonlinear Wave Equation 62%
  • Invariant Measure 53%

• Modulation spaces with scaling symmetry

  Benyi, A. & Oh, T., 31 Jan 2020, In: Applied and Computational Harmonic Analysis. 48, 1, p. 496–507 12 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Modulation Spaces 100%
  • Multiplier 66%
  • Function Space 66%
  • Scaling 63%
  • Modulation 57%
• 2019

  Quasi-invariant Gaussian measures for the cubic nonlinear Schrödinger equation with third order dispersion

  Oh, T., Tsutsumi, Y. & Tzvetkov, N., 23 Apr 2019, In: Comptes Rendus Mathématique. 357, 4, p. 366-381 16 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Gauge Transformation 100%
  • Cubic equation 94%
  • Gaussian Measure 90%
  • Invariant Measure 71%
  • Nonlinear Equations 61%

• On the probabilistic Cauchy theory for nonlinear dispersive PDEs

  Benyi, A., Oh, T. & Pocovnicu, O., 31 Jan 2019, Landscapes of Time-Frequency Analysis, Applied and Numerical Harmonic Analysis . Birkhäuser, p. 1-32 32 p. (Applied and Numerical Harmonic Analysis).

  Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

  Open Access

  • Cauchy 100%
  • Well-posedness 99%
  • Partial differential equation 81%
  • Review 81%
• 2018

  On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle

  Oh, T. & Wang, Y., 31 Dec 2018, In: Analele Ştiinţifice ale Universităţii "Alexandru Ioan Cuza'' din Iaşi - Matematică (Annals of the Alexandru Ioan Cuza University - Mathematics). 64, 1, p. 53-84 32 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Cubic equation 100%
  • Ill-posedness 98%
  • Circle 65%
  • Nonlinear Equations 65%
  • Inflation 48%

• An optimal regularity result on the quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation

  Oh, T., Sosoe, P. & Tzvetkov, N., 30 Oct 2018, In: Journal de l’École polytechnique — Mathématiques (JEP). 5, p. 793-841 49 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Quasi-invariance 100%
  • Fourth-order Equations 78%
  • Gaussian Measure 77%
  • Invariant Measure 61%
  • Nonlinear Equations 52%

• Renormalization of the two-dimensional stochastic nonlinear wave equations

  Oh, T., Gubinelli, M. & Koch, H., Oct 2018, In: Transactions of the American Mathematical Society. 370, 10, p. 7335-7359 25 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Stochastic Wave Equation 100%
  • Wave equations 89%
  • Renormalization 79%
  • Nonlinear Wave Equation 77%
  • Space-time White Noise 32%

• A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations

  Oh, T. & Thomann, L., Sep 2018, In: Stochastics and Partial Differential Equations: Analysis and Computations. 6, 3, p. 397-445 49 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Gibbs Measure 100%
  • Nonlinear equations 90%
  • Invariant Measure 79%
  • Nonlinear Equations 67%
  • Polynomials 64%

• Global well-posedness of the periodic cubic fourth order NLS in negative Sobolev spaces

  Oh, T. & Wang, Y., 11 May 2018, In: Forum of Mathematics, Sigma. 6, p. 1-80 80 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Sobolev space 100%
  • Global Well-posedness 65%
  • Energy Functional 62%
  • Fourth Order 52%
  • Sobolev Spaces 51%

• Global, decaying solutions of a focusing energy-critical heat equation in R^4

  Gustafson, S. & Roxanas, D., 5 May 2018, In: Journal of Differential Equations. 264, 9, p. 5894-5927 41 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Rigidity 100%
  • Navier Stokes equations 97%
  • Global Solution 92%
  • Heat Equation 91%
  • Dissipate 76%

• Non-existence of solutions for the periodic cubic NLS below L^2

  Oh, T. & Guo, Z., 20 Mar 2018, In: International Mathematics Research Notices. 2018, 6, p. 1656-1729 74 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Cubic equation 100%
  • Nonexistence 69%
  • Fourier Restriction Norm 66%
  • Nonlinear Equations 65%
  • A Priori Bounds 48%
• 2017

  Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation

  Oh, T. & Tzvetkov, N., Dec 2017, In: Probability theory and related fields. 169, 3-4, p. 1121-1168 48 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Fourth-order Equations 100%
  • Gaussian Measure 99%
  • Invariant Measure 78%
  • Sobolev Spaces 72%
  • Circle 67%

• Normal form approach to global well-posedness of the quadratic derivative nonlinear Schrödinger equation on the circle

  Chung, J., Guo, Z., Kwon, S. & Oh, T., 26 Sep 2017, In: Annales de l'Institut Henri Poincaré C. 34, 5, p. 1273-1297 25 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Global Well-posedness 100%
  • Nonlinear equations 97%
  • nonlinear equations 85%
  • Normal Form 79%
  • Derivatives 74%

• A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting

  Oh, T. & Pocovnicu, O., 12 Sep 2017, In: Tohoku mathematical journal. 69, 3, p. 455-481 27 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Global Well-posedness 100%
  • Nonlinear Wave Equation 99%
  • Energy 60%

• A remark on norm inflation with general initial data for the cubic nonlinear Schrödinger equations in negative Sobolev spaces

  Oh, T., 13 Jul 2017, In: Funkcialaj ekvacioj-Serio internacia. 60, 2, p. 259-277 19 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Cubic equation 100%
  • Ill-posedness 98%
  • Inflation 96%
  • Sobolev Spaces 70%
  • Scaling 69%

• Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on ℝ^3

  Killip, R., Oh, T., Pocovnicu, O. & Visan, M., Jul 2017, In: Archive for Rational Mechanics and Analysis. 225, 1, p. 469-548 80 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Solitons 100%
  • Quintic 82%
  • Nonlinear equations 76%
  • Scattering 66%
  • Nonlinear Equations 57%
• 2016

  On invariant Gibbs measures for the generalized KdV equations

  Oh, T., Richards, G. & Thomann, L., 23 Jun 2016, In: Dynamics of Partial Differential Equations. 13, 2, p. 133-153 21 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Generalized KdV Equation 100%
  • Gibbs Measure 82%
  • White noise 76%
  • Invariant Measure 65%
  • Polynomials 53%

• On the transport of Gaussian measures under the flow of Hamiltonian PDEs

  Oh, T. & Tzvetkov, N., 17 May 2016, Séminaire Laurent Schwartz — EDP et applications. Vol. 6. 9 p.

  Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

  Open Access

  File

  • Gaussian Measure 100%

• Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on ℝ^3

  Oh, T. & Pocovnicu, O., 2 Mar 2016, In: Journal de Mathématiques Pures et Appliquées. 105, 3, p. 342-366 25 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Wave equations 100%
  • Quintic 92%
  • Global Well-posedness 87%
  • Nonlinear Wave Equation 86%
  • Energy 53%
• 2015

  On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ^d, d ≥ 3

  Benyi, A., Oh, T. & Pocovnicu, O., 26 May 2015, In: Transactions of the American Mathematical Society: Series B. 2, p. 1-50 50 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Cubic equation 100%
  • Global Well-posedness 89%
  • Cauchy 71%
  • Nonlinear Equations 65%
  • Regularity 42%