Multilinear estimates with applications to nonlinear Schrödinger and Hartree equations in Lp^-spaces

Ryosuke Hyakuna

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper is concerned with the Cauchy problem of the Schrödinger equation with polynomial-type nonlinearities and the Hartree equation. It is shown that these Cauchy problems are locally well posed in (Formula presented.) under certain conditions on p, where (Formula presented.)Local solutions are constructed in a function space based on the fundamental theorem of calculus and the free Schrödinger group (Formula presented.), which was originally used by YI.Zhou.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalJournal of Evolution Equations
DOIs
Publication statusAccepted/In press - 2018 Mar 1

Fingerprint

Hartree Equation
Lp Spaces
Nonlinear Equations
Cauchy Problem
Fundamental theorem of calculus
Estimate
Local Solution
Free Group
Function Space
Nonlinearity
Polynomial

Keywords

  • Cauchy problem
  • Hartree equation
  • Local well-posedness
  • Nonlinear Schrödinger equations

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Multilinear estimates with applications to nonlinear Schrödinger and Hartree equations in Lp^-spaces. / Hyakuna, Ryosuke.

In: Journal of Evolution Equations, 01.03.2018, p. 1-16.

Research output: Contribution to journalArticle

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