Singular Stochastic Dispersive Dynamics

Project Information

SingStocDispDyn

Grant agreement ID: 864138

DOI

10.3030/864138

EC signature date 15 January 2020

Start date 1 March 2020

End date 28 February 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 920 968,00

EU contribution

€ 1 920 968,00

Coordinated by

THE UNIVERSITY OF EDINBURGH
United Kingdom

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Other (25)

Sharp quasi-invariance threshold for the cubic Szegő equation

Author(s): James Coe, Leonardo Tolomeo
Published in: 2024
Publisher: arXiv

On the inviscid limit of the singular stochastic complex Ginzburg-Landau equation at statistical equilibrium

Author(s): Younes Zine
Published in: 2022
Publisher: arXiv

Local well-posedness of the periodic nonlinear Schrödinger equation with a quadratic nonlinearity $\overline{u}^2$ in negative Sobolev spaces

Author(s): Ruoyuan Liu
Published in: 2022
Publisher: arXiv

Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity

Author(s): Ilya Chevyrev, Tadahiro Oh, Yuzhao Wang
Published in: 2022
Publisher: arXiv

Norm inflation for the derivative nonlinear Schrödinger equation

Author(s): Yuzhao Wang, Younes Zine
Published in: 2022
Publisher: arXiv

Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space

Author(s): Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov, Nicola Visciglia
Published in: 2023
Publisher: arXiv

Norm inflation with infinite loss of regularity for the generalized improved Boussinesq equation

Author(s): Pierre de Roubin
Published in: 2023
Publisher: arXiv

Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus

Author(s): Andreia Chapouto, Guopeng Li, Ruoyuan Liu
Published in: 2023
Publisher: arXiv

Global well-posedness of one-dimensional cubic fractional nonlinear Schrödinger equations in negative Sobolev spaces

Author(s): Enguerrand Brun, Guopeng Li, Ruoyuan Liu, Younes Zine
Published in: 2023
Publisher: arXiv

Stochastic quantization of the Φ^3_3-model

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

Invariant measures for the periodic KdV and mKdV equations using complete integrability

Author(s): Andreia Chapouto, Justin Forlano
Published in: 2023
Publisher: arXiv

Hyperbolic P(Φ)_2-model on the plane

Author(s): Tadahiro Oh, Leonardo Tolomeo, Yuzhao Wang, Guangqu Zheng
Published in: 2022
Publisher: arXiv

Existence, uniqueness, and universality of global dynamics for the fractional hyperbolic Φ^4_3-model

Author(s): Ruoyuan Liu, Nikolay Tzvetkov, Yuzhao Wang
Published in: 2023
Publisher: arXiv

A note on products of stochastic objects

Author(s): Tadahiro Oh, Younes Zine
Published in: Kyoto Journal of Mathematics, 2022, ISSN 2156-2261
Publisher: Duke University Press

Quasi-invariance of Gaussian measures of negative regularity for fractional nonlinear Schrödinger equations

Author(s): Justin Forlano, Leonardo Tolomeo
Published in: 2022
Publisher: arXiv

Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation

Author(s): Guopeng Li, Liying Tao, Tengfei Zhao
Published in: 2024
Publisher: arXiv

Stochastic quantization of Liouville conformal field theory

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

Invariant measures for mKdV and KdV in infinite volume

Author(s): Justin Forlano, Rowan Killip, Monica Visan
Published in: 2024
Publisher: arXiv

Smoluchowski-Kramers approximation for the singular stochastic wave equations in two dimensions

Author(s): Younes Zine
Published in: 2022
Publisher: arXiv

Optimal divergence rate of the focusing Gibbs measure

Author(s): Guopeng Li, Rui Liang, Yuzhao Wang
Published in: 2023
Publisher: arXiv

Compact T(1) theorem à la Stein

Author(s): Árpád Bényi, Guopeng Li, Tadahiro Oh, Rodolfo H. Torres
Published in: 2024
Publisher: arXiv

On the deep-water and shallow-water limits of the intermediate long wave equation from a statistical viewpoint

Author(s): Guopeng Li, Tadahiro Oh, Guangqu Zheng
Published in: 2022
Publisher: arXiv

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

Author(s): Tadahiro Oh, Mamoru Okamoto, Leonardo Tolomeo
Published in: Memoir of the American Mathematical Society, 2021, ISSN 1947-6221
Publisher: American Mathematicakl Society

Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus

Author(s): Guopeng Li, Mamoru Okamoto, Liying Tao
Published in: 2024
Publisher: arXiv

Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation

Author(s): Justin Forlano, Leonardo Tolomeo
Published in: 2024
Publisher: arXiv

Peer reviewed articles (35)

A remark on randomization of a general function of negative regularity

Author(s): Tadahiro Oh, Mamoru Okamoto, Oana Pocovnicu, Nikolay Tzvetkov
Published in: Proceedings of the American Mathematical Society, Series B, Issue 11, 2024, Page(s) 538-554, ISSN 2330-1511
Publisher: American Mathematical Society
DOI: 10.1090/bproc/241

Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations

Author(s): Ruoyuan Liu
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, Issue 12, 2024, Page(s) 898-931, ISSN 2194-0401
Publisher: Springer
DOI: 10.1007/s40072-023-00297-7

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, 2021, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnab084

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

Author(s): Tadahiro Oh, Yuzhao Wang
Published in: Discrete & Continuous Dynamical Systems, Issue 41/6, 2021, Page(s) 2971, ISSN 1553-5231
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2020393

Discrete bilinear operators and commutators

Author(s): Árpád Bényi, Tadahiro Oh
Published in: The Journal of Geometric Analysis, Issue 33, 2023, ISSN 1559-002X
Publisher: Springer
DOI: 10.1007/s12220-022-01136-2

Almost conservation laws for stochastic nonlinear Schrödinger equations

Author(s): Kelvin Cheung, Guopeng Li, Tadahiro Oh
Published in: Journal of Evolution Equations, Issue 21/2, 2021, Page(s) 1865-1894, ISSN 1424-3199
Publisher: Birkhauser Verlag
DOI: 10.1007/s00028-020-00659-x

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, Issue 9/1, 2021, Page(s) 1-32, ISSN 2194-0401
Publisher: Springer Verlag
DOI: 10.1007/s40072-020-00165-8

Fractional Leibniz rule on the torus

Author(s): Árpád Bényi, Tadahiro Oh, Tengfei Zhao
Published in: Proceedings of the American Mathematical Society, Issue 153, 2024, Page(s) 207-221, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/17007

Intermediate long wave equation in negative Sobolev spaces

Author(s): Andreia Chapouto, Justin Forlano, Guopeng Li, Tadahiro Oh, Didier Pilod
Published in: Proceedings of the American Mathematical Society, Series B, Issue 11, 2024, Page(s) 452-468, ISSN 2330-1511
Publisher: American Mathematica Society
DOI: 10.1090/bproc/206

Global well-posedness of the energy-critical stochastic nonlinear wave equations

Author(s): Enguerrand Brun, Guopeng Li, Ruoyuan Liu
Published in: Journal of Differential Equations, Issue 397, 2024, Page(s) 316-348, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2024.03.032

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, Issue 11, 2024, Page(s) 420-460, ISSN 2330-0000
Publisher: American Mathematical Society
DOI: 10.1090/btran/178

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

Author(s): Tadahiro Oh, Yuzhao Wang, Younes Zine
Published in: Stochastics and Partial Differential Equations: Analysis and Computations volume, Issue 21940401, 2022, ISSN 2194-0401
Publisher: Springer
DOI: 10.1007/s40072-022-00237-x

Compact bilinear operators and paraproducts revisited

Author(s): Árpád Bényi, Guopeng Li, Tadahiro Oh, Rodolfo H. Torres
Published in: Canadian Mathematical Bulletin, Issue 68, 2025, Page(s) 44-59, ISSN 0008-4395
Publisher: Canadian Mathematical Society
DOI: 10.4153/s000843952400047x

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, Issue 151/5, 2021, Page(s) 1450-1466, ISSN 0308-2105
Publisher: The RSE Scotland Foundation
DOI: 10.1017/prm.2020.68

Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid–structure interaction

Author(s): Jeffrey Kuan, Tadahiro Oh, Sunčica Čanić
Published in: Applicable Analysis, Issue 00036811, 2022, ISSN 0003-6811
Publisher: Taylor & Francis
DOI: 10.1080/00036811.2022.2103682

On the probabilistic well-posedness of the two-dimensional periodic nonlinear Schrödinger equation with the quadratic nonlinearity |u|^2

Author(s): Ruoyuan Liu
Published in: Journal de Mathématiques Pures et Appliquées, Issue 171, 2023, Page(s) 75-101, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2022.12.010

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

Author(s): Tadahiro Oh, Mamoru Okamoto
Published in: Electronic Journal of Probability, Issue 26/none, 2021, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/20-ejp575

Solving the 4NLS with white noise initial data

Author(s): Tadahiro Oh, Nikolay Tzvetkov, Yuzhao Wang
Published in: Forum of Mathematics, Sigma, Issue 8, 2020, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2020.51

On the Parabolic and Hyperbolic Liouville Equations

Author(s): Tadahiro Oh, Tristan Robert, Yuzhao Wang
Published in: Communications in Mathematical Physics, 2021, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-04125-8

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 00209910, 2022, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-021-01080-y

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

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

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, Issue 26900998, 2022, ISSN 2690-0998
Publisher: Mathematical Science Publishers
DOI: 10.2140/pmp.2022.3.343

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, Issue 130/9, 2020, Page(s) 5838-5864, ISSN 0304-4149
Publisher: Elsevier BV
DOI: 10.1016/j.spa.2020.05.010

Stochastic nonlinear wave dynamics on compact surfaces

Author(s): Tadahiro Oh, Tristan Robert, Nikolay Tzvetkov
Published in: Annales Henri Lebesgue, Issue 6, 2023, Page(s) 161-223, ISSN 2644-9463
Publisher: École Normale Supérieure de Rennes
DOI: 10.5802/ahl.163

On the two-dimensional singular stochastic viscous nonlinear wave equations

Author(s): Ruoyuan Liu, Tadahiro Oh
Published in: Comptes Rendus Mathématique, Issue 360, 2022, Page(s) 1227-1248, ISSN 1778-3569
Publisher: Académie des sciences, Institut de France
DOI: 10.5802/crmath.377

Deep-water and shallow-water limits of the intermediate long wave equation

Author(s): Guopeng Li
Published in: Nonlinearity, Issue 37, 2024, Page(s) 075001, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ad4843

On the local linearization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing

Author(s): Jingyu Huang, Tadahiro Oh, Mamoru Okamoto
Published in: Proceedings of the American Mathematical Society, Series B, Issue 11, 2024, Page(s) 378-389, ISSN 2330-1511
Publisher: American Mathematical Society
DOI: 10.1090/bproc/226

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, Issue 03730956, 2022, ISSN 0373-0956
Publisher: Association des Annales de I'Institut Fourier
DOI: 10.5802/aif.3454

Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces

Author(s): Tadahiro Oh, Kihoon Seong
Published in: Journal of Functional Analysis, Issue 281/9, 2021, Page(s) 109150, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2021.109150

Sharp local well-posedness of the two-dimensional periodic nonlinear Schrödinger equation with a quadratic nonlinearity $|u|^2$

Author(s): Ruoyuan Liu, Tadahiro Oh
Published in: Mathematical Research Letters, Issue 31, 2024, Page(s) 255-277, ISSN 1073-2780
Publisher: Mathematical Publishing
DOI: 10.4310/mrl.240904213416

Deep-water limit of the intermediate long wave equation in $L^2$

Author(s): Andreia Chapouto, Guopeng Li, Tadahiro Oh, Didier Pilod
Published in: Mathematical Research Letters, Issue 31, 2025, Page(s) 1655-1692, ISSN 1073-2780
Publisher: Mathematical Publishing
DOI: 10.4310/mrl.250210231602

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, Issue 60, 2024, ISSN 0246-0203
Publisher: Elsevier BV
DOI: 10.1214/23-aihp1380

A remark on Gibbs measures with log-correlated Gaussian fields

Author(s): Tadahiro Oh, Kihoon Seong, Leonardo Tolomeo
Published in: Forum of Mathematics, Sigma, Issue 12, 2024, Page(s) 1-40, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2024.28

Norm inflation for the viscous nonlinear wave equation

Author(s): Pierre de Roubin, Mamoru Okamoto
Published in: Nonlinear Differential Equations and Applications NoDEA, Issue 31, 2024, ISSN 1021-9722
Publisher: Birkhauser Verlag
DOI: 10.1007/s00030-024-00944-5

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`, Issue 375, 2022, Page(s) 8483-8528, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8699

Non-peer reviewed articles (1)

Unconditional deep-water limit of the intermediate long wave equation in low-regularity

Author(s): Justin Forlano, Guopeng Li, Tengfei Zhao
Published in: Nonlinear Differential Equations and Applications NoDEA, Issue 32, 2025, ISSN 1021-9722
Publisher: Birkhauser Verlag
DOI: 10.1007/s00030-025-01037-7