Uniqueness of solutions for zakharov systems

Nader Masmoudi, Kenji Nakanishi

Research output: Contribution to journalArticle

Abstract

We prove that the weak solution of the Cauchy problem for the Klein-Gordon-Zakharov system and for the Zakharov system is unique in the energy space for the former system, and in some larger space for the latter system, in dimensions three or lower. In the three dimensional case, these are the largest Sobolev spaces where the local wellposedness has been proven so far. Our proof uses infinite iteration, where the solution is fixed but the function spaces are converging to the desired ones in the limit.

Original languageEnglish (US)
Pages (from-to)233-253
Number of pages21
JournalFunkcialaj Ekvacioj
Volume52
Issue number2
DOIs
StatePublished - Aug 2009

Fingerprint

Uniqueness of Solutions
Local Well-posedness
Function Space
Sobolev Spaces
Weak Solution
Three-dimension
Cauchy Problem
Iteration
Three-dimensional
Energy

Keywords

  • Unconditional uniqueness
  • Zakharov system

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Uniqueness of solutions for zakharov systems. / Masmoudi, Nader; Nakanishi, Kenji.

In: Funkcialaj Ekvacioj, Vol. 52, No. 2, 08.2009, p. 233-253.

Research output: Contribution to journalArticle

Masmoudi, Nader ; Nakanishi, Kenji. / Uniqueness of solutions for zakharov systems. In: Funkcialaj Ekvacioj. 2009 ; Vol. 52, No. 2. pp. 233-253.
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