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Sub-critical well-posedness for the intermediate nonlinear Schrödinger equation on the line
Andreia Chapouto, Justin Forlano, Thierry Laurens
We continue our study of the well-posedness theory for the intermediate nonlinear Schrödinger equation (INLS). Firstly, we prove that INLS is locally well-posed in $H^s (\mathbb{R}…
Well-posedness for the periodic Intermediate nonlinear Schrödinger equation
Andreia Chapouto, Justin Forlano, Thierry Laurens
We study the well-posedness for the intermediate nonlinear Schrödinger equation (INLS) with periodic boundary conditions. Using a gauge transform, we obtain large data local well-p…
Gauge transform for the Korteweg-de Vries equation and well-posedness below the -scale
Andreia Chapouto, Simão Correia, João Pedro Ramos
We propose a new formulation of the Korteweg-de Vries equation (KdV) on the real line, via a gauge transform. While KdV and the gauged equation are equivalent for smooth solutions,…
On the well-posedness of the intermediate nonlinear Schrödinger equation on the line
Andreia Chapouto, Justin Forlano, Thierry Laurens
We consider a family of intermediate nonlinear Schrödinger equations (INLS) on the real line, which includes the continuum Calogero-Moser models (CCM). We prove that INLS is locall…
A continuum of invariant measures for the periodic KdV and mKdV equations
Andreia Chapouto, Justin Forlano
We consider the real-valued defocusing modified Korteweg-de Vries equation (mKdV) on the circle. Based on the complete integrability of mKdV, Killip-Vişan-Zhang (2018) discovered a…
Invariance of the Gibbs measures for periodic generalized Korteweg-de Vries equations
Andreia Chapouto, Nobu Kishimoto
In this paper, we study the Gibbs measures for periodic generalized Korteweg-de Vries equations (gKdV) with quartic or higher nonlinearities. In order to bypass the analytical ill-…
A refined well-posedness result for the modified KdV equation in the Fourier-Lebesgue spaces
Andreia Chapouto
We study the well-posedness of the complex-valued modified Korteweg-de Vries equation (mKdV) on the circle at low regularity. In our previous work (2019), we introduced the second…
A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces
Andreia Chapouto
We study the complex-valued modified Korteweg-de Vries equation (mKdV) on the circle. We first consider the real-valued setting and show global well-posedness of the (usual) renorm…