ORBITAL STABILITY OF SOLITARY WAVES FOR THE GENERALIZED CHOQUARD MODEL

Vladimir Georgiev; Mirko Tarulli; George Venkov

ORBITAL STABILITY OF SOLITARY WAVES FOR THE GENERALIZED CHOQUARD MODEL

Vladimir Georgiev, Mirko Tarulli, George Venkov

Graduate School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the generalized Choquard equation describing trapped electron gas in 3 dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. In equivalent way one can optimize the Gagliardo–Nirenberg inequality subject to the constraint fixing the L² norm. The uniqueness of the minimizers for the case p = 2, i.e. for the case of Hartree–Choquard is well known. The main difficulty for the case p > 2 is connected with possible lack of control on the L^p norm of the minimizers.

MSC Codes 37K40, 35Q55, 35Q51

Original language	English
Journal	Unknown Journal
Publication status	Published - 2019 Aug 21

Keywords

Generalized Choquard equation
Ground states
Local uniqueness

ASJC Scopus subject areas

General

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title = "ORBITAL STABILITY OF SOLITARY WAVES FOR THE GENERALIZED CHOQUARD MODEL",

abstract = "We consider the generalized Choquard equation describing trapped electron gas in 3 dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. In equivalent way one can optimize the Gagliardo–Nirenberg inequality subject to the constraint fixing the L2 norm. The uniqueness of the minimizers for the case p = 2, i.e. for the case of Hartree–Choquard is well known. The main difficulty for the case p > 2 is connected with possible lack of control on the Lp norm of the minimizers.MSC Codes 37K40, 35Q55, 35Q51",

keywords = "Generalized Choquard equation, Ground states, Local uniqueness",

author = "Vladimir Georgiev and Mirko Tarulli and George Venkov",

year = "2019",

month = aug,

day = "21",

language = "English",

journal = "Nuclear Physics A",

issn = "0375-9474",

publisher = "Elsevier",

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TY - JOUR

T1 - ORBITAL STABILITY OF SOLITARY WAVES FOR THE GENERALIZED CHOQUARD MODEL

AU - Georgiev, Vladimir

AU - Tarulli, Mirko

AU - Venkov, George

PY - 2019/8/21

Y1 - 2019/8/21

N2 - We consider the generalized Choquard equation describing trapped electron gas in 3 dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. In equivalent way one can optimize the Gagliardo–Nirenberg inequality subject to the constraint fixing the L2 norm. The uniqueness of the minimizers for the case p = 2, i.e. for the case of Hartree–Choquard is well known. The main difficulty for the case p > 2 is connected with possible lack of control on the Lp norm of the minimizers.MSC Codes 37K40, 35Q55, 35Q51

AB - We consider the generalized Choquard equation describing trapped electron gas in 3 dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. In equivalent way one can optimize the Gagliardo–Nirenberg inequality subject to the constraint fixing the L2 norm. The uniqueness of the minimizers for the case p = 2, i.e. for the case of Hartree–Choquard is well known. The main difficulty for the case p > 2 is connected with possible lack of control on the Lp norm of the minimizers.MSC Codes 37K40, 35Q55, 35Q51

KW - Generalized Choquard equation

KW - Ground states

KW - Local uniqueness

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JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

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