Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

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Publications

On the unique ergodicity for a class of 2 dimensional stochastic wave equations

Author(s): Justin Forlano, Leonardo Tolomeo
Published in: Transactions of the American Mathematical Society, 2024, Page(s) 345–394, ISSN 1088-6850
Publisher: American Mathematical Society
DOI: 10.1090/tran/8973

Global well-posedness of the 4-d energy-critical stochastic nonlinear Schrödinger equations with non-vanishing boundary condition

Author(s): Kelvin Cheung, Guopeng Li
Published in: Funkcialaj Ekvacioj, 2022, Page(s) 287-309, ISSN 0532-8721
Publisher: Mathematical Society of Japan
DOI: 10.1619/fesi.65.287

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

Author(s): Tadahiro Oh, Philippe Sosoe, Leonardo Tolomeo
Published in: Inventiones mathematicae, Issue 227, 2022, Page(s) 1323-1429, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-021-01080-y

Invariance of the Gibbs measures for periodic generalized Korteweg-de Vries equations

Author(s): Andreia Chapouto, Nobu Kishimoto
Published in: Transactions of the American Mathematical Society, 2022, Page(s) 8483–8528, ISSN 1088-6850
Publisher: American Mathematical Society
DOI: 10.1090/tran/8699

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

Author(s): Tadahiro Oh, Philippe Sosoe, Nikolay Tzvetkov
Published in: Journal de l’École polytechnique — Mathématiques, Issue 5, 2018, Page(s) 793-841, ISSN 2270-518X
Publisher: École polytechnique
DOI: 10.5802/jep.83

On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities

Author(s): Tadahiro Oh, Mamoru Okamoto, Oana Pocovnicu
Published in: Discrete & Continuous Dynamical Systems - A, Issue 39/6, 2019, Page(s) 3479-3520, ISSN 1553-5231
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2019144

Higher order expansions for the probabilistic local Cauchy theory of the cubic nonlinear Schrödinger equation on $\mathbb {R}^3$

Author(s): Árpád Bényi, Tadahiro Oh, Oana Pocovnicu
Published in: Transactions of the American Mathematical Society, Series B, Issue 6/4, 2019, Page(s) 114-160, ISSN 2330-0000
Publisher: American Mathematical Society
DOI: 10.1090/btran/29

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

Author(s): Tadahiro Oh, Laurent Thomann
Published in: Annales de la Faculté des Sciences de Toulouse, 2020, ISSN 0240-2963
Publisher: Universite Toulouse
DOI: 10.5802/afst.1620

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

Author(s): Tadahiro Oh, Nikolay Tzvetkov
Published in: Journal of the European Mathematical Society, Issue 22/6, 2020, Page(s) 1785-1826, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/956

Renormalization of the two-dimensional stochastic nonlinear wave equations

Author(s): Massimiliano Gubinelli, Herbert Koch, Tadahiro Oh
Published in: Transactions of the American Mathematical Society, Issue 370/10, 2017, Page(s) 1, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7452

GLOBAL WELL-POSEDNESS OF THE PERIODIC CUBIC FOURTH ORDER NLS IN NEGATIVE SOBOLEV SPACES

Author(s): TADAHIRO OH, YUZHAO WANG
Published in: Forum of Mathematics, Sigma, Issue 6, 2018, Page(s) 1-80, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2018.4

Solving the 4NLS with white noise initial data

Author(s): Tadahiro Oh, Nikolay Tzvetkov, Yuzhao Wang
Published in: Forum of Mathematics, Sigma, 2020, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2020.51

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

Author(s): Tadahiro Oh, Yoshio Tsutsumi, Nikolay Tzvetkov
Published in: Comptes Rendus Mathematique, Issue 357/4, 2019, Page(s) 366-381, ISSN 1631-073X
Publisher: Elsevier Masson
DOI: 10.1016/j.crma.2019.04.001

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

Author(s): Tadahiro Oh, Oana Pocovnicu, Yuzhao Wang
Published in: Kyoto Journal of Mathematics, 2020, Page(s) 1227-1243, ISSN 2156-2261
Publisher: Duke University Press
DOI: 10.1215/21562261-2019-0060

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

Author(s): Soonsik Kwon, Tadahiro Oh, Haewon Yoon
Published in: Annales de la Faculté des Sciences de Toulouse, 2020, ISSN 0240-2963
Publisher: Universite Toulouse
DOI: 10.5802/afst.1643

STOCHASTIC NONLINEAR SCHRÖDINGER EQUATION WITH ALMOST SPACE–TIME WHITE NOISE

Author(s): JUSTIN FORLANO, TADAHIRO OH, YUZHAO WANG
Published in: Journal of the Australian Mathematical Society, 2019, Page(s) 1-24, ISSN 1446-7887
Publisher: Australian Mathematical Society
DOI: 10.1017/s1446788719000156

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

Author(s): Tadahiro Oh, Oana Pocovnicu
Published in: Tohoku Mathematical Journal, Issue 69/3, 2017, Page(s) 455-481, ISSN 0040-8735
Publisher: Tohoku University
DOI: 10.2748/tmj/1505181626

Non-Existence of Solutions for the Periodic Cubic NLS below ${L}^{{2}}$

Author(s): Zihua Guo, Tadahiro Oh
Published in: International Mathematics Research Notices, Issue 2018, no. 6, 2018, Page(s) rnw271, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnw271

On invariant Gibbs measures for the generalized KdV equations

Author(s): Tadahiro Oh, Geordie Richards, Laurent Thomann
Published in: Dynamics of Partial Differential Equations, Issue 13/2, 2016, Page(s) 133-153, ISSN 1548-159X
Publisher: International Press
DOI: 10.4310/DPDE.2016.v13.n2.a3

"Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on <mml:math altimg=""si1.gif"" overflow=""scroll"" xmlns:xocs=""http://www.elsevier.com/xml/xocs/dtd"" xmlns:xs=""http://www.w3.org/2001/XMLSchema"" xmlns:xsi=""http://www.w3.org/2001/XMLSchema-instance"" xmlns=""http://www.elsevier.com/xml/ja/dtd"" xmlns:ja=""http://www.elsevier.com/xml/ja/dtd"" xmlns:mml=""ht"

Author(s): Tadahiro Oh, Oana Pocovnicu
Published in: Journal de Mathématiques Pures et Appliquées, Issue 105/3, 2016, Page(s) 342-366, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2015.11.003

A Remark on Norm Inflation with General Initial Data for the Cubic Nonlinear Schrödinger Equations in Negative Sobolev Spaces

Author(s): Tadahiro Oh
Published in: Funkcialaj Ekvacioj, Issue 60/2, 2017, Page(s) 259-277, ISSN 0532-8721
Publisher: Mathematical Society of Japan
DOI: 10.1619/fesi.60.259

On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on $\mathbb {R}^d$, $d \geq 3$

Author(s): Árpád Bényi, Tadahiro Oh, Oana Pocovnicu
Published in: Transactions of the American Mathematical Society, Series B, Issue 2/1, 2015, Page(s) 1-50, ISSN 2330-0000
Publisher: American Mathematical Society
DOI: 10.1090/btran/6

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

Author(s): Tadahiro Oh, Yuzhao Wang
Published in: "Analele Ştiinţifice ale Universităţii ""Alexandru Ioan Cuza'' din Iaşi - Matematică (Annals of the Alexandru Ioan Cuza University - Mathematics)", Issue 64/1, 2018, Page(s) 53-84, ISSN 1221-8421
Publisher: Editura Universitatea Alexendru Ion Cuza

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

Author(s): Jaywan Chung, Zihua Guo, Soonsik Kwon, Tadahiro Oh
Published in: Annales de l'Institut Henri Poincare (C) Non Linear Analysis, Issue 34, 2016, Page(s) 1273–1297, ISSN 0294-1449
Publisher: Elsevier BV
DOI: 10.1016/j.anihpc.2016.10.003

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

Author(s): Tadahiro Oh, Laurent Thomann
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, Issue 6, 2018, Page(s) 1-49, ISSN 2194-0401
Publisher: Springer Verlag
DOI: 10.1007/s40072-018-0112-2

Solitons and Scattering for the Cubic–Quintic Nonlinear Schrödinger Equation on $${\mathbb{R}^3}$$ R 3

Author(s): Rowan Killip, Tadahiro Oh, Oana Pocovnicu, Monica Vişan
Published in: Archive for Rational Mechanics and Analysis, Issue 225/1, 2017, Page(s) 469-548, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-017-1109-0

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

Author(s): Tadahiro Oh, Nikolay Tzvetkov
Published in: Probability Theory and Related Fields, Issue 169/3-4, 2017, Page(s) 1121-1168, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-016-0748-7

Modulation spaces with scaling symmetry

Author(s): Árpád Bényi, Tadahiro Oh
Published in: Applied and Computational Harmonic Analysis, Issue 48/1, 2020, Page(s) 496-507, ISSN 1063-5203
Publisher: Academic Press
DOI: 10.1016/j.acha.2019.04.005

Stochastic nonlinear wave dynamics on compact surfaces

Author(s): Tadahiro Oh, Tristan Robert, Nikolay Tzvetkov
Published in: Annales Henri Lebesgue, 2023, Page(s) 161-223, ISSN 2644-9463
Publisher: Centre Mersenne
DOI: 10.5802/ahl.163

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

Author(s): Trishen S. Gunaratnam, Tadahiro Oh, Nikolay Tzvetkov, Hendrik Weber
Published in: Probability and Mathematical Physics, 2022, Page(s) 343–379, ISSN 2690-1005
Publisher: Mathematical Sciences Publisher
DOI: 10.2140/pmp.2022.3.343

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

Author(s): Tadahiro Oh, Oana Pocovnicu, Nikolay Tzvetkov
Published in: Annales de l'Institut Fourier, 2022, Page(s) 771-830, ISSN 1777-5310
Publisher: Centre Mersenne
DOI: 10.5802/aif.3454

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

Author(s): Gubinelli, Massimiliano; Koch, Herbert; Oh, Tadahiro
Published in: Journal of the European Mathematical Society, 2023, ISSN 1435-9863
Publisher: EMS Press
DOI: 10.4171/jems/1294

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

Author(s): Tadahiro Oh, Mamoru Okamoto, Tristan Robert
Published in: Stochastic Processes and their Applications, 2020, Page(s) 5838–5864, ISSN 0304-4149
Publisher: Elsevier BV
DOI: 10.1016/j.spa.2020.05.010

On the parabolic and hyperbolic Liouville equations

Author(s): Tadahiro Oh, Tristan Robert, Yuzhao Wang
Published in: Communications in Mathematical Physics, 2021, Page(s) 1281–1351, ISSN 1432-0916
Publisher: Springer Nature
DOI: 10.1007/s00220-021-04125-8

On the two-dimensional hyperbolic stochastic sine-Gordon equation

Author(s): Tadahiro Oh, Tristan Robert, Philippe Sosoe, Yuzhao Wang
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, 2020, ISSN 2194-0401
Publisher: Springer Verlag
DOI: 10.1007/s40072-020-00165-8

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

Author(s): Tadahiro Oh, Mamoru Okamoto
Published in: Electronic Journal of Probability, 2021, Page(s) 1-44, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-ejp575

On the stochastic nonlinear Schrödinger equations at critical regularities

Author(s): Tadahiro Oh, Mamoru Okamoto
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, 2020, ISSN 2194-0401
Publisher: Springer Verlag
DOI: 10.1007/s40072-019-00163-5

Unique Ergodicity for a Class of Stochastic Hyperbolic Equations with Additive Space-Time White Noise

Author(s): Leonardo Tolomeo
Published in: Communications in Mathematical Physics, 2020, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-020-03752-x

Normal form approach to the one-dimensional periodic cubic nonlinear Schrödinger equation in almost critical Fourier-Lebesgue spaces

Author(s): Tadahiro Oh, Yuzhao Wang
Published in: Journal d'Analyse Mathematique, 2021, Page(s) 723–762, ISSN 1565-8538
Publisher: Springer Link
DOI: 10.1007/s11854-021-0168-1

On the transport of Gaussian measures under the one-dimensional fractional nonlinear Schrödinger equations

Author(s): Justin Forlano, William J. Trenberth
Published in: Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019, ISSN 0294-1449
Publisher: Elsevier BV
DOI: 10.1016/j.anihpc.2019.07.006

"Almost sure global well posedness for the BBM equation with infinite <inline-formula><tex-math id=""M1"">\begin{document}$ L^{2} $\end{document}</tex-math></inline-formula> initial data"

Author(s): Justin Forlano
Published in: Discrete & Continuous Dynamical Systems - A, Issue 40/1, 2020, Page(s) 267-318, ISSN 1553-5231
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2020011

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

Author(s): Tadahiro Oh, Yuzhao Wang
Published in: Discrete and Continuous Dynamical Systems, 2021, Page(s) 2971-2992, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2020393

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

Author(s): Tadahiro Oh, Yuzhao Wang
Published in: Journal of Differential Equations, Issue 269/1, 2020, Page(s) 612-640, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2019.12.017

Almost conservation laws for stochastic nonlinear Schrödinger equations

Author(s): Kelvin Cheung, Guopeng Li, Tadahiro Oh
Published in: Journal of Evolution Equations, 2021, Page(s) 1865–1894, ISSN 1424-3199
Publisher: Birkhauser Verlag
DOI: 10.1007/s00028-020-00659-x

Invariant Gibbs dynamics for the dynamical sine-Gordon model

Author(s): Tadahiro Oh, Tristan Robert, Philippe Sosoe, Yuzhao Wang
Published in: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2021, Page(s) 1450-1466, ISSN 0308-2105
Publisher: The RSE Scotland Foundation
DOI: 10.1017/prm.2020.68

Global dynamics for the two-dimensional stochastic nonlinear wave equations

Author(s): Massimiliano Gubinelli, Herbert Koch, Tadahiro Oh, Leonardo Tolomeo
Published in: International Mathematics Research Notices, 2022, Page(s) 16954--16999, ISSN 1687-0247
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnab084

A remark on norm inflation for nonlinear wave equations

Author(s): Justin Forlano, Mamoru Okamoto
Published in: Dynamics of Partial Differential Equations, 2020, Page(s) 361 – 381, ISSN 1548-159X
Publisher: International Press
DOI: 10.4310/dpde.2020.v17.n4.a3

Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain

Author(s): Leonardo Tolomeo
Published in: Annals of Probability, 2021, Page(s) 1402-1426, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-aop1484

A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces

Author(s): Andreia Chapouto
Published in: Discrete and Continuous Dynamical Systems, 2021, Page(s) 3915–3950, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2021022

A dichotomy concerning uniform boundedness of Riesz transforms on Riemannian manifolds

Author(s): Alex Amenta, Leonardo Tolomeo
Published in: Proceedings of the American Mathematical Society, Issue 147/11, 2019, Page(s) 4797-4803, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/14730

Global dynamics for the stochastic KdV equation with white noise as initial data

Author(s): Tadahiro Oh, Jeremy Quastel, Philippe Sosoe
Published in: Transactions of the American Mathematical Society Series B, 2024, Page(s) 420-460, ISSN 2330-0000
Publisher: American Mathematical Society
DOI: 10.1090/btran/178

An L^p-theory for almost sure local well-posedness of the nonlinear Schrödinger equations

Author(s): Oana Pocovnicu, Yuzhao Wang
Published in: Comptes Rendus Mathematique, 2018, Page(s) 637-643, ISSN 1631-073X
Publisher: Elsevier Masson
DOI: 10.1016/j.crma.2018.04.009

A refined well-posedness result for the modified KdV equation in the Fourier-Lebesgue spaces

Author(s): Andreia Chapouto
Published in: Journal of Dynamics and Differential Equations, 2023, Page(s) 2537–2578, ISSN 1572-9222
Publisher: Springer Link
DOI: 10.1007/s10884-021-10050-0

Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations

Author(s): Justin Forlano, Kihoon Seong
Published in: Communications in Partial Differential Equations, 2022, Page(s) 1296-1337, ISSN 1532-4133
Publisher: Taylor and Francis Ltd.
DOI: 10.1080/03605302.2022.2053861

Focusing Φ^4_3-model with a Hartree-type nonlinearity

Author(s): Tadahiro Oh, Mamoru Okamoto, Leonardo Tolomeo
Published in: Memoirs of the American Mathematical Society, 2020
Publisher: arXiv

Uniqueness and non-uniqueness of the Gaussian free field evolution under the two-dimensional Wick ordered cubic wave equation

Author(s): Tadahiro Oh, Mamoru Okamoto, Nikolay Tzvetkov
Published in: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2022
Publisher: arXic

Stochastic quantization of Liouville conformal field theory

Author(s): Tadahiro Oh, Tristan Robert, Nikolay Tzvetkov, Yuzhao Wang
Published in: 2020
Publisher: arXiv

Stochastic quantization of the Φ^3_3-model

Author(s): Tadahiro Oh, Mamoru Okamoto, Leonardo Tolomeo
Published in: 2021
Publisher: arXiv

On the Probabilistic Cauchy Theory for Nonlinear Dispersive PDEs

Author(s): Árpád Bényi, Tadahiro Oh, Oana Pocovnicu
Published in: Landscapes of Time-Frequency Analysis, 2019, Page(s) 1-32, ISBN 978-3-030-05209-6
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-05210-2_1

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

Author(s): Tadahiro Oh, Nikolay Tzvetkov
Published in: Séminaire Laurent Schwartz — EDP et applications, 2015, Page(s) 1-9, ISSN 2266-0607
Publisher: les Éditions de l'École polytechnique
DOI: 10.5802/slsedp.84

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