Tadahiro (Choonghong) Oh

Papers by group members (partially) supported under my ERC Consolidator Grant "SingStocDispDyn" (2020-2026):

  1. J. Forlano Improved quasi-invariance result for the periodic Benjamin-Ono-BBM equation.
  2. J. Forlano (with L. Tolomeo) Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation.
  3. J. Coe (with L. Tolomeo) Sharp quasi-invariance threshold for the cubic Szegő equation.
  4. G. Li (with M. Okamoto, L. Tao) Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus.
  5. J. Forlano, G. Li (with T. Zhao), Unconditional deep-water limit of the intermediate long wave equation in low-regularity, to appear in NoDEA Nonlinear Differential Equations Appl.
  6. G. Li (with L. Tao, T. Zhao), Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation.
  7. J. Forlano (with R. Killip, M. Vişan), Invariant measures for mKdV and KdV in infinite volume.
  8. G. Li, R. Liu, Y. Zine (with E. Brun), Global well-posedness of the one-dimensional fractional cubic nonlinear Schrödinger equations.
  9. G. Li, R. Liu (with E. Brun), Global well-posedness of the energy-critical stochastic nonlinear wave equations, J. Differential Equations. 397 (2024), 316--348.
  10. R. Liu (with N. Tzvetkov, Y. Wang), Existence, uniqueness, and universality of global dynamics for the fractional hyperbolic Φ 43 -model.
  11. A. Chapouto, G. Li, R. Liu, Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus, to appear in Proc. Roy. Soc. Edinburgh Sect. A.
  12. G. Li (with R. Liang, Y. Wang), Optimal divergence rate of the focusing Gibbs measure.
  13. P. de Roubin (with M. Okamoto), Norm inflation for the viscous nonlinear wave equation, NoDEA Nonlinear Differential Equations Appl. 31, 52 (2024). https://doi.org/10.1007/s00030-024-00944-5
  14. P. de Roubin, Norm inflation with infinite loss of regularity for the generalized improved Boussinesq equation.
  15. A. Chapouto, J. Forlano, Invariant measures for the periodic KdV and mKdV equations using complete integrability.
  16. J. Forlano (with L. Tolomeo), Quasi-invariance of Gaussian measures of negative regularity for fractional nonlinear Schrödinger equations, to appear in J. Eur. Math. Soc.
  17. R. Liu (with A. Debussche, N. Tzvetkov, N. Visciglia), Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space, Probab. Theory Related Fields 189 (2024), no. 3-4, 1161--1218.
  18. Y. Zine (with T. Robert), Stochastic complex Ginzburg-Landau equation on compact surfaces.
  19. Y. Zine, On the inviscid limit of the singular stochastic complex Ginzburg-Landau equation at statistical equilibrium.
  20. R. Liu, Local well-posedness of the periodic nonlinear Schrödinger equation with a quadratic nonlinearity u2 in negative Sobolev spaces, J. Dynam. Differential Equations (2023) https://doi.org/10.1007/s10884-023-10295-x
  21. G. Li, Deep-water and shallow-water limits of the intermediate long wave equation, Nonlinearity 37 (2024), no. 7, Paper No. 075001, 44 pp.
  22. Y. Zine, Smoluchowski-Kramers approximation for the singular stochastic wave equations in two dimensions.
  23. Y. Zine (with Y. Wang), Norm inflation for the derivative nonlinear Schrödinger equation, C. R. Math. Acad. Sci. Paris 362 (2024), 1857--1871.
  24. R. Liu, On the probabilistic well-posedness of the two-dimensional periodic nonlinear Schrödinger equation with the quadratic nonlinearity |u|2 (arXiv link), J. Math. Pures Appl. 171 (2023), 75--101.
  25. R. Liu, Global well-posedness of the two-dimensional random viscous nonlinear wave equations, Stoch. Partial Differ. Equ. Anal. Comput. 12 (2024), no. 2, 898--931.

Papers by group members (partially) supported under my ERC Starting Grant "ProbDynDispEq" (2015-2020):

  1. J. Forlano (with K. Seong), Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations, Comm. Partial Differential Equations 47 (2022), no. 6, 1296--1337.
  2. J. Forlano (with L. Tolomeo), On the unique ergodicity for a class of 2 dimensional stochastic wave equations, Trans. Amer. Math. Soc. 377 (2024), no. 1, 345--394.
  3. A. Chapouto (with N. Kishimoto), Invariance of the Gibbs measures for periodic generalized Korteweg-de Vries equations, Trans. Amer. Math. Soc. 375 (2022), no. 12, 8483--8528.
  4. A. Chapouto, A refined well-posedness result for the modified KdV equation in the Fourier-Lebesgue spaces, J. Dynam. Differential Equations 35 (2023), no. 3, 2537--2578.
  5. L. Tolomeo, Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain (arXiv link), Ann. Probab. 49 (2021), 1402--1426.
  6. K. Cheung (with O. Pocovnicu), Local well-posedness of stochastic nonlinear Schrödinger equations on ℝd with supercritical noise.
  7. A. Chapouto, A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces, Discrete Contin. Dyn. Syst. A, 41 (2021), no. 8, 3915--3950.
  8. L. Tolomeo (with R. Mosincat, O. Pocovnicu, Y. Wang), Global well-posedness of three-dimensional periodic stochastic nonlinear beam equations.
  9. K. Cheung, G. Li, Global well-posedness of the 4-d energy-critical stochastic nonlinear Schrödinger equations with non-vanishing boundary condition, Funkcial. Ekvac. 65 (2022), no. 3, 287--309.
  10. J. Forlano (with M. Okamoto) A remark on norm inflation for nonlinear wave equations, Dyn. Partial Differ. Equ. 17 (2020), no. 4, 361--381.
  11. L. Tolomeo, Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise (arXiv link), Comm. Math. Phys. 377 (2020), 1311--1347.
  12. J. Forlano, Almost sure global well-posedness of the BBM equation with infinite L2 initial data, Discrete Contin. Dyn. Syst. A. 40 (2020), 267--318.
  13. L. Tolomeo (with A. Amenta), A dichotomy concerning uniform boundedness of Riesz transforms on Riemannian manifolds (arXiv link), Proc. Amer. Math. Soc. 147 (2019), no. 11, 4797--4803.
  14. J. Forlano (with W.J. Trenberth), On the transport of Gaussian measures under the one-dimensional fractional nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 7, 1987--2025.
  15. Y. Wang (with O. Pocovnicu), An Lp-theory for almost sure local well-posedness of the nonlinear Schrödinger equations, C. R. Math. Acad. Sci. Paris 356 (2018), no. 6, 637--643.