The program was following in JST (Japan Standard Time, UTC+9):
August 24th (wed), 2022
| 09:50--10:00 | Opening | |
| 10:00--10:40 | Carlos Kenig✶1 | (University of Chicago) |
| The method of energy channels for wave equations | ||
| 10:50--11:30 | Mitsuru Sugimoto | (Nagoya University) |
| A constructive approach to nonlinear wave equations | ||
| 11:40--12:20 | Hideo Takaoka | (Kobe University) |
| Bilinear Strichartz estimates for the KdV equation on the torus | ||
| 14:00--14:40 | Naoyasu Kita | (Kumamoto University) |
| L2-decay rate of solutions to dissipative nonlinear Schrödinger equations | ||
| 14:50--15:30 | Kotaro Tsugawa | (Chuo University) |
| Well-posedness and parabolic smoothing effect for higher order Schrödinger type equations with constant coefficients | ||
| 15:50--16:30 | Masahito Ohta | (Tokyo University of Science) |
| On cubic-quintic nonlinear Schrödinger equations with delta potential | ||
| 16:40--17:20 | Piero D'Ancona ✶2 ♯1 | (Sapienza University of Rome) |
| Scattering for the NLS with variable coefficients on the line | ||
August 25th (thu), 2022
| 10:00--10:40 | Gustavo Ponce✶3 | (University of California, Santa Barbara) |
| On local energy decay for solution of the Benjamin-Ono equation | ||
| 10:50--11:30 | Hideo Kubo | (Hokkaido University) |
| On the Rellich type inequality for Schrödinger operators with potential of inverse-square type | ||
| 11:40--12:20 | Hiroyuki Takamura | (Tohoku University) |
| The combined effect in one space dimension beyond the general theory for nonlinear wave equations | ||
| 14:00--14:40 | Takayoshi Ogawa | (Tohoku University) |
| Initial boundary value problem for nonlinear Schrödinger equations in low dimensional half-space | ||
| 14:50--15:30 | Yonggeun Cho✶4♯2 | (Jeonbuk National University) |
| Global well-posedness of Hartree type Dirac equations at critical regularity | ||
| 15:50--16:30 | Nicola Visciglia✶5 | (University of Pisa) |
| Global existence for NLS with multiplicative white noise on 𝐓2 | ||
| 16:40--17:20 | Vladimir Georgiev ♯3 | (University of Pisa) |
| On global existence of solutions for periodic NLS with non-gauge invariant quadratic nonlinearity | ||
| 19:00-- | Online Banquet | |
August 26th (fri), 2022
| 10:00--10:40 | Jalal M. I. Shatah✶6 | (New York University) |
| Wave Turbulance | ||
| 10:50--11:30 | Kenji Nakanishi | (Kyoto University) |
| Global dynamics around multi-solitons for nonlinear Klein-Gordon equations | ||
| 11:40--12:20 | Hironobu Sasaki | (Chiba University) |
| The scattering problem for nonlinear Klein-Gordon equations with rapidly decreasing input data | ||
| 14:00--14:40 | Hideaki Sunagawa | (Osaka Metropolitan University) |
| Upper and lower L2-decay bounds for a class of derivative nonlinear Schrödinger equations | ||
| 14:50--15:30 | Masahiro Ikeda | (RIKEN, Keio University) |
| On stability and instability of standing waves for 2d-nonlinear Schrödinger equations with point interaction | ||
| 15:50--16:30 | Yuta Wakasugi | (Hiroshima University) |
| Blow-up of solutions of semilinear wave equations in Friedmann-Lemaitre-Robertson-Walker spacetime | ||
| 16:30--16:40 | Closing | |
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Talks marked by ✶ are delivered remotely via Zoom at the following local time:
✶1 20:00--20:40 August 23rd in CDT(Central Daylight Time, UTC-5)
✶2 09:40--10:20 August 24th in CEST(Central European Summer Time, UTC+2)
✶3 18:00--18:40 August 24th in PDT(Pacific Daylight Time, UTC-7)
✶4 14:50--15:30 August 25th in KST(Korea Standard Time, UTC+9)
✶5 08:50--09:30 August 25th in CEST(Central European Summer Time, UTC+2)
✶6 21:00--21:40 August 25th in EDT(Eastern Daylight Time, UTC-4)
✶1 20:00--20:40 August 23rd in CDT(Central Daylight Time, UTC-5)
✶2 09:40--10:20 August 24th in CEST(Central European Summer Time, UTC+2)
✶3 18:00--18:40 August 24th in PDT(Pacific Daylight Time, UTC-7)
✶4 14:50--15:30 August 25th in KST(Korea Standard Time, UTC+9)
✶5 08:50--09:30 August 25th in CEST(Central European Summer Time, UTC+2)
✶6 21:00--21:40 August 25th in EDT(Eastern Daylight Time, UTC-4)
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Abstracts for talks marked by ♯:
♯1 In recent years an efficient framework was established to prove scattering for nonlinear dispersive equations, based on the combination of concentration-compactness principles and induction on energy arguments. Originally developed by Kenig and Merle, the framework has been adapted to several equations with constant coefficients. The presence of potential perturbations or variable coefficients introduces new difficulties due to unisotropy. In this talk I shall report on some new results, obtained in collaboration with Angelo Zanni (Roma), concerning scattering for a defocusing, subcritical NLS in one space dimension, with fully variable coefficients.
♯2 In this talk I will introduce a recent result on the global well-posedness of classical Dirac equation with Hartree type nonlinearity in 𝐑1+3. The equation is essentially L2-critical. A standard argument is to utilize spinorial null structure inside the equations. However, the null structure is not enough to attain the global well-posedness at critical regularity. I will impose an extra regularity assumption with respect to the angular variable to prove global well-posedness and scattering of Dirac equations for small L2x-data with additional angular regularity. This talk is based on the joint work with S. Hong and T. Ozawa.
♯3 The work is a collaboration with prof. Tohru Ozawa and prof. Kazumasa Fujiwara. We study 1D NLS with non-gauge invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global solutions which are constant with respect to space. The non-existence of global solutions also has been studied only by focusing on the behavior of the Fourier 0 mode of solutions. However, the earlier works are not sufficient to obtain the precise criteria for the global existence for the Cauchy problem. In this paper, the exact criteria for the global existence of L2 solutions is shown by studying the interaction between the Fourier 0 mode and oscillation of solutions. Namely, L2 solutions are shown a priori not to exist globally if they are different from the trivial ones.
♯1 In recent years an efficient framework was established to prove scattering for nonlinear dispersive equations, based on the combination of concentration-compactness principles and induction on energy arguments. Originally developed by Kenig and Merle, the framework has been adapted to several equations with constant coefficients. The presence of potential perturbations or variable coefficients introduces new difficulties due to unisotropy. In this talk I shall report on some new results, obtained in collaboration with Angelo Zanni (Roma), concerning scattering for a defocusing, subcritical NLS in one space dimension, with fully variable coefficients.
♯2 In this talk I will introduce a recent result on the global well-posedness of classical Dirac equation with Hartree type nonlinearity in 𝐑1+3. The equation is essentially L2-critical. A standard argument is to utilize spinorial null structure inside the equations. However, the null structure is not enough to attain the global well-posedness at critical regularity. I will impose an extra regularity assumption with respect to the angular variable to prove global well-posedness and scattering of Dirac equations for small L2x-data with additional angular regularity. This talk is based on the joint work with S. Hong and T. Ozawa.
♯3 The work is a collaboration with prof. Tohru Ozawa and prof. Kazumasa Fujiwara. We study 1D NLS with non-gauge invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global solutions which are constant with respect to space. The non-existence of global solutions also has been studied only by focusing on the behavior of the Fourier 0 mode of solutions. However, the earlier works are not sufficient to obtain the precise criteria for the global existence for the Cauchy problem. In this paper, the exact criteria for the global existence of L2 solutions is shown by studying the interaction between the Fourier 0 mode and oscillation of solutions. Namely, L2 solutions are shown a priori not to exist globally if they are different from the trivial ones.
