Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation

被引：0

作者：

Camps, Nicolas ^{[1
]}

Gassot, Louise ^{[2
]}

Ibrahim, Slim ^{[3
,4
]}

机构：

[1] Univ Paris Saclay, Lab Math Orsay, CNRS, UMR 8628, Batiment 307, F-91405 Orsay, France

[2] Univ Basel, Dept Math & Informat, Spiegelgasse 1, CH-4051 Basel, Switzerland

[3] Univ Victoria, Dept Math & Stat, 3800 Finnerty Rd, Victoria, BC V8P 5C2, Canada

[4] Pacific Inst Math Sci, 4176-2207 Main Mall, Vancouver, BC V6T 1Z4, Canada

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 380卷

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

Cauchy theory; Nonlinear Schrodinger equation; Half-wave equation; Weakly dispersive equation; Random initial data; Quasilinear equation; NONLINEAR SCHRODINGER-EQUATION; DATA CAUCHY-THEORY; GLOBAL EXISTENCE; SCATTERING;

D O I：

10.1016/j.jde.2023.10.054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain probabilistic local well-posedness in quasilinear regimes for the Schrodinger half-wave equation with a cubic nonlinearity. We need to use a refined ansatz because of the lack of probabilistic smoothing in the Picard's iterations, which is due to the high-low-low nonlinear interactions. The proof is an adaptation of the method of Bringmann on the derivative nonlinear wave equation [6] to Schrodinger-type equations. In addition, we discuss ill-posedness results for this equation. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：443 / 490

页数：48

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