On Hartree equations with derivatives

Yonggeun Cho; Sanghyuk Lee; Tohru Ozawa

doi:10.1016/j.na.2010.11.015

On Hartree equations with derivatives

Yonggeun Cho^*
, Sanghyuk Lee
, Tohru Ozawa

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

6 Scopus citations

Abstract

We consider the Cauchy problem of two types of Hartree equations with exchangecorrelation correction terms: {iu_t - Δu = V _k(u)u in ℝ¹⁺ⁿ, k = 1,2,u(0) = φ in ℝⁿ, n ≥ 1, where V₁(u) = |x|^-γ*₁|u|² + λ₂|∇u| ²),V₂(u) = |x|^-γ *∥∇|^δu|²). We establish the well-posedness of Cauchy problems and show the smoothing effect of solutions for each 0 < γ < n and 0 ≤ δ ≤ 1.

Original language	English
Pages (from-to)	2094-2108
Number of pages	15
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	74
Issue number	6
DOIs	https://doi.org/10.1016/j.na.2010.11.015
State	Published - 2011.03.15

Keywords

Angular regularity
Hartree equations with derivatives
Smoothing effect
Well-posedness

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1016/j.na.2010.11.015

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@article{9c446213e4fd479e89a5f0585d3d49c2,

title = "On Hartree equations with derivatives",

abstract = "We consider the Cauchy problem of two types of Hartree equations with exchangecorrelation correction terms: \{iut - Δu = V k(u)u in ℝ1+n, k = 1,2,u(0) = φ in ℝn, n ≥ 1, where V1(u) = |x|-γ*1|u|2 + λ2|∇u| 2),V2(u) = |x|-γ *∥∇|δu|2). We establish the well-posedness of Cauchy problems and show the smoothing effect of solutions for each 0 < γ < n and 0 ≤ δ ≤ 1.",

keywords = "Angular regularity, Hartree equations with derivatives, Smoothing effect, Well-posedness",

author = "Yonggeun Cho and Sanghyuk Lee and Tohru Ozawa",

year = "2011",

month = mar,

day = "15",

doi = "10.1016/j.na.2010.11.015",

language = "English",

volume = "74",

pages = "2094--2108",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

number = "6",

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TY - JOUR

T1 - On Hartree equations with derivatives

AU - Cho, Yonggeun

AU - Lee, Sanghyuk

AU - Ozawa, Tohru

PY - 2011/3/15

Y1 - 2011/3/15

N2 - We consider the Cauchy problem of two types of Hartree equations with exchangecorrelation correction terms: {iut - Δu = V k(u)u in ℝ1+n, k = 1,2,u(0) = φ in ℝn, n ≥ 1, where V1(u) = |x|-γ*1|u|2 + λ2|∇u| 2),V2(u) = |x|-γ *∥∇|δu|2). We establish the well-posedness of Cauchy problems and show the smoothing effect of solutions for each 0 < γ < n and 0 ≤ δ ≤ 1.

AB - We consider the Cauchy problem of two types of Hartree equations with exchangecorrelation correction terms: {iut - Δu = V k(u)u in ℝ1+n, k = 1,2,u(0) = φ in ℝn, n ≥ 1, where V1(u) = |x|-γ*1|u|2 + λ2|∇u| 2),V2(u) = |x|-γ *∥∇|δu|2). We establish the well-posedness of Cauchy problems and show the smoothing effect of solutions for each 0 < γ < n and 0 ≤ δ ≤ 1.

KW - Angular regularity

KW - Hartree equations with derivatives

KW - Smoothing effect

KW - Well-posedness

UR - https://www.scopus.com/pages/publications/79951813303

U2 - 10.1016/j.na.2010.11.015

DO - 10.1016/j.na.2010.11.015

M3 - Journal article

AN - SCOPUS:79951813303

SN - 0362-546X

VL - 74

SP - 2094

EP - 2108

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 6

ER -

On Hartree equations with derivatives

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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