ORBITAL STABILITY OF SOLITARY WAVES FOR THE GENERALIZED CHOQUARD MODEL

Vladimir Georgiev, Mirko Tarulli, George Venkov

Research output: Contribution to journalArticlepeer-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 Lp norm of the minimizers.

MSC Codes 37K40, 35Q55, 35Q51

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Aug 21

Keywords

  • Generalized Choquard equation
  • Ground states
  • Local uniqueness

ASJC Scopus subject areas

  • General

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