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

Ryosuke Hyakuna

doi:10.1007/s00028-018-0432-8

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

Ryosuke Hyakuna^*

^*Corresponding author for this work

Waseda Research Institute for Science and Engineering

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

4 Citations (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 language	English
Pages (from-to)	1-16
Number of pages	16
Journal	Journal of Evolution Equations
DOIs	https://doi.org/10.1007/s00028-018-0432-8
Publication status	Accepted/In press - 2018 Mar 1

Keywords

Cauchy problem
Hartree equation
Local well-posedness
Nonlinear Schrödinger equations

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1007/s00028-018-0432-8

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abstract = "This paper is concerned with the Cauchy problem of the Schr{\"o}dinger 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 Schr{\"o}dinger group (Formula presented.), which was originally used by YI.Zhou.",

keywords = "Cauchy problem, Hartree equation, Local well-posedness, Nonlinear Schr{\"o}dinger equations",

author = "Ryosuke Hyakuna",

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doi = "10.1007/s00028-018-0432-8",

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AB - 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.

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KW - Hartree equation

KW - Local well-posedness

KW - Nonlinear Schrödinger equations

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

Abstract

Keywords

ASJC Scopus subject areas

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