Masayuki Hayashi

activity

20232025

collaborators

4 papers

math.AP2025

Uniqueness of solutions for the logarithmic Schrödinger equation

Masayuki Hayashi

We consider the Cauchy problem for the logarithmic Schrödinger equation and prove uniqueness of weak $H^{s} (R^{d})$ solutions for $s \in (0, 1)$ , which improves on the previous u…

math.AP2024

Global $H^{2}$ -solutions for the generalized derivative NLS on $T$

Masayuki Hayashi, Tohru Ozawa, Nicola Visciglia

We prove global existence of $H^{2}$ solutions to the Cauchy problem for the generalized derivative nonlinear Schrödinger equation on the 1-d torus. This answers an open problem pose…

math.AP2023

Low regularity solutions to the logarithmic Schrodinger equation

Rémi Carles, Masayuki Hayashi, Tohru Ozawa

We consider the logarithmic Schr{ö}dinger equation, in various geometric settings. We show that the flow map can be uniquely extended from H^1 to L^2 , and that this extension is L…

math.AP2023

The Cauchy problem for the logarithmic Schrödinger equation revisited

Masayuki Hayashi, Tohru Ozawa

We revisit the Cauchy problem for the logarithmic Schrödinger equation and construct strong solutions in $H^{1}$ , the energy space, and the $H^{2}$ -energy space. The solutions are prov…

Uniqueness of solutions for the logarithmic Schrödinger equation

Global H2-solutions for the generalized derivative NLS on T

Low regularity solutions to the logarithmic Schrodinger equation

The Cauchy problem for the logarithmic Schrödinger equation revisited

Global $H^{2}$ -solutions for the generalized derivative NLS on $T$