Research

Research Interest

Well-posedness and Large time behavior of solutions to Nonlinear Dispersive Equations

非線型分散型偏微分方程式における解の適切性と時間大域挙動の解明

Refereed Papers

1. Satoshi Masaki and Hayato Miyazaki, Global behavior of solutions to generalized Gross-Pitaevskii equation, Differential Equations and Dynamical Systems 32, 743-761 (2024). [Link | arXiv]

2. Masaki Kawamoto and Hayato Miyazaki, Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials, Journal of Differential Equations 365 (2023) 127-167. [Link | arXiv]

3. Kazuki Aoki, Takahisa Inui, Hayato Miyazaki, Haruya Mizutani and Kota Uriya, Asymptotic behavior for the long-range nonlinear Schrödinger equation on star graph with the Kirchhoff boundary condition, Pure and Applied Analysis 4-2 (2022), 287-311. [Link | arXiv]

4. Hayato Miyazaki, Local well-posedness for the higher-order generalized KdV type equation with low-degree of nonlinearity, to appear in RIMS Kôkyûroku Bessatsu. [arXiv]

5. Hayato Miyazaki, Strong blow-up instability for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations, Discrete & Continuous Dynamical Systems, 41 (2021), no. 5, 2411-2445. [Link | arXiv]

6. Hayato Miyazaki and Motohiro Sobajima, Lifespan of solutions to nonlinear Schrödinger equations with general homogeneous nonlinearity of the critical order, Advances in Harmonic Analysis and Partial Differential Equations (2020), pp. 197-207. [Link | arXiv]

7. Hayato Miyazaki, Lower bound for the lifespan of solutions to the generalized KdV equation with low-degree of nonlinearity, Advanced Studies in Pure Mathematics 85 (2020), The Role of Metrics in the Theory of Partial Differential Equations, pp. 303-313. [Link]

8. Felipe Linares, Hayato Miyazaki and Gustavo Ponce, On a class of solutions to the generalized KdV type equation, Communications in Contemporary Mathematics 21 (2019), no.7, 1850056, 21 pp. [Link | arXiv]

9. Satoshi Masaki, Hayato Miyazaki and Kota Uriya, Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions, Transactions of the American Mathematical Society 371 (2019), no. 11, 7925-7947. [Link | arXiv]

10. Satoshi Masaki and Hayato Miyazaki, Nonexistence of scattering and modified scattering states for some nonlinear Schrödinger equation with critical homogeneous nonlinearity, Differential and Integral Equations 32 (2019), no. 3-4, 121-138. [Link | arXiv]

11. Satoshi Masaki and Hayato Miyazaki, Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity, SIAM Journal on Mathematical Analysis 50 (2018), no. 3, 3251–3270. [Link | arXiv]

12. Kazumasa Fujiwara and Hayato Miyazaki, The derivation of conservation laws for nonlinear Schrödinger equations with power type nonlinearities, RIMS Kôkyûroku Bessatsu B63 (2017), 13-21.  [Link] (Previous version [arXiv])

13. Hayato Miyazaki, The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity, Journal of Mathematical Analysis and Applications 417 (2014), no. 2 580-600. [Link | arXiv]

Preprints

1. Masaki Kawamoto and Hayato Miyazaki, Modified scattering operator for nonlinear Schrödinger equations with time-decaying harmonic potentials, submitted. [arXiv]

2. Kazuki Aoki, Takahisa Inui, Hayato Miyazaki, Haruya Mizutani and Kota Uriya, Modified scattering for inhomogeneous nonlinear Schrödinger equations with and without inverse-square potential, submitted. [arXiv]

Non-refereed Proceedings

1. Hayato Miyazaki, Improvement of a regularity condition for long-range scattering for NLS with critical homogeneous nonlinearity, RIMS Kôkyûroku, No.2257. [Link]

2. 空間遠方で消滅しない境界条件をもつ非線型シュレディンガー方程式のエネルギー解について, 第36回発展方程式若手セミナー報告集, 2014年12月, p175-182 (in Japanese).

3. 空間遠方で消滅しない初期値をもつ非線形Schrödinger方程式における保存則について, 第35回発展方程式若手セミナー報告集, 2013年12月, p79-84 (in Japanese).

Talks

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