Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity

2014/02/21 by Younghun Hong, Hong, Younghun, Kenneth Taliaferro +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1402.5347

openalex publication_date 2014/02/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy on ℝ^d in a low regularity Sobolev type space. More precisely, we reduce the regularity s down to the currently known regularity requirement for unconditional uniqueness of solutions to the cubic nonlinear Schrödinger equation (s≥(d)/(6) if d=1,2 and s>s_c=(d-2)/(2) if d≥ 3). In such a way, we extend the recent work of Chen-Hainzl-Pavlović-Seiringer.

Citations

• Space‐time estimates for null forms and the local existence theorem
• On nonlinear Schrödinger equations, II.H S -solutions and unconditional well-posedness
• Derivation of a Nonlinear Schrödinger Equation with a General power-type nonlinerity

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