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20182026
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math.AP2026

Fefferman--Stein-type estimates and fractional NLS in Fourier Sobolev spaces

Divyang G. Bhimani, Ryosuke Hyakuna

In this paper, we prove a sharp Fefferman--Stein-type estimate for the fractional Schrödinger equation, which can be regarded as a generalized Strichartz estimate for data in the F…

math.AP2025

Global well-posedness for the 1D cubic nonlinear Schrödinger equation in

Ryosuke Hyakuna

In this paper, we show that the one dimensional cubic nonlinear Schrödinger equation is globally well posed in for . In particular, we prove that the global sol…

math.AP2024

Unconditional well-posedness for the nonlinear Schrödinger equation in Bessel potential spaces

Ryosuke Hyakuna

The Cauchy problem for the nonlinear Schrödinger equation is called unconditionally well posed in a data space if it is well posed in the usual sense and the solution is unique…

math.AP2022

Well-posedness for the 1D cubic nonlinear Schrödinger equation in ,

Ryosuke Hyakuna

In this paper, local well-posedness is shown for the one dimensional cubic nonlinear Schrödinger equation in -spaces for , which generalizes a classical result for $p=2…

math.AP2018

Well-posedness and decay estimates for 1D nonlinear Schrödinger equations with Cauchy data in

Ryosuke Hyakuna

In this paper, we establish a standard -theory of solutions to one dimensional nonlinear Schrödinger equations with the power like nonlinearity. More precisely, we extend the…