8 papers
Small-data theory for the intermediate NLS and the Calogero--Moser derivative NLS
Sonae Hadama
In this paper, we study a class of nonlinear Schrödinger equations (NLS) in a unified way. This class includes two important examples: the intermediate NLS (INLS) and the Calogero…
Applications of renormalisation to orthonormal Strichartz estimates and the NLS system on the circle
Sonae Hadama, Andrew Rout
In this paper, we introduce a renormalisation procedure for the density associated with the system of nonlinear Schrödinger equations (NLSS) on a circle. We show that this renorma…
Well-posedness in the full scaling-subcritical range for a class of nonlocal NLS on the line
Sonae Hadama
In this paper, we study a class of one-dimensional nonlocal nonlinear Schrödinger equations on the line with nonlinearity given by a Fourier multiplier whose symbol has subcritica…
Probabilistic Strichartz estimates in Schatten classes and their applications to the Hartree equation
Sonae Hadama, Takuto Yamamoto
In this paper, we consider the Strichartz estimates for orthonormal systems in the context of randomization. Frank, Lewin, Lieb, and Seiringer first proved the orthonormal Strichar…
Semi-classical limit of quantum scattering states for the nonlinear Hartree equation
Sonae Hadama, Younghun Hong
This article concerns the long-time dynamics of quantum particles in the semi-classical regime. First, we show that for the nonlinear Hartree equation with short-range interaction…
Uniform dispersive estimates for the semi-classical Hartree equation with long-range interaction
Sonae Hadama
In this paper, we consider the Hartree equation with smooth but long-range interaction in the semi-classical regime, in three-dimensional space. We show that the density function o…