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Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

Publications

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
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
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
DOI: 10.1090/btran/29

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
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
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
DOI: 10.1017/fms.2018.4

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
DOI: 10.1016/j.crma.2019.04.001

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
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
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
DOI: 10.4310/DPDE.2016.v13.n2.a3

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
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
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

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
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
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
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
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
DOI: 10.1016/j.acha.2019.04.005

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
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
DOI: 10.3934/dcds.2020011

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
DOI: 10.1090/proc/14730

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, 2017

Sovling the 4NLS with white noise initial data

Author(s): Tadahiro Oh, Nikolay Tzvetkov, Yuzhao Wang
Published in: 2018

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, 2018

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, 2018

Stochastic nonlinear wave dynamics on compact surfaces

Author(s): Tadahiro Oh, Tristan Robert, Nikolay Tzvetkov
Published in: 2019

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: 2018

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

Author(s): Tadahiro Oh, Oana Pocovnicu, Nikolay Tzvetkov
Published in: 2019

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

Author(s): Gubinelli, Massimiliano; Koch, Herbert; Oh, Tadahiro
Published in: 2018

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, 2019

On the parabolic and hyperbolic Liouville equations

Author(s): Tadahiro Oh, Tristan Robert, Yuzhao Wang
Published in: 2019

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

Author(s): Tadahiro Oh, Mamoru Okamoto
Published in: 2019

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, 2018

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

Author(s): Tadahiro Oh, Yuzhao Wang
Published in: 2018

Almost conservation laws for stochastic nonlinear Schrödinger equations

Author(s): Kelvin Cheung, Guopeng Li, Tadahiro Oh
Published in: 2019

Invariant Gibbs dynamics for the dynamical sine-Gordon model

Author(s): Tadahiro Oh, Tristan Robert, Philippe Sosoe, Yuzhao Wang
Published in: 2020

Stochastic quantization of Liouville conformal field theory

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

Global dynamics for the two-dimensional stochastic nonlinear wave equations

Author(s): Massimiliano Gubinelli, Herbert Koch, Tadahiro Oh, Leonardo Tolomeo
Published in: 2020

A remark on norm inflation for nonlinear wave equations

Author(s): Justin Forlano, Mamoru Okamoto
Published in: 2019

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

Author(s): Leonardo Tolomeo
Published in: 2019

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

Author(s): Andreia Chapouto
Published in: 2019

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
DOI: 10.1007/978-3-030-05210-2_1

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
DOI: 10.1017/s1446788719000156

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
DOI: 10.5802/slsedp.84

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
DOI: 10.1007/s40072-020-00165-8

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
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
DOI: 10.1007/s00220-020-03752-x

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
DOI: 10.1016/j.jde.2019.12.017