On mass concentration for the L2-critical nonlinear schrodinger equations

M. Chae; S. Hong; J. Kim; S. Lee; C. W. Yang

doi:10.1080/03605300902812426

On mass concentration for the L²-critical nonlinear schrodinger equations

M. Chae, S. Hong, J. Kim, S. Lee, C. W. Yang

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

6 Citations (Scopus)

Abstract

We consider the mass concentration phenomenon for the L²-critical nonlinear Schrödinger equations. We show the mass concentration of blow-up solutions contained in L^q_tL^r_x space near the finite time. The new ingredient in this paper is a refinement of Strichartz's estimates with the mixed norm L^q_tL^r_x for 2<q≤r.

Original language	English
Pages (from-to)	486-505
Number of pages	20
Journal	Communications in Partial Differential Equations
Volume	34
Issue number	5
DOIs	https://doi.org/10.1080/03605300902812426
Publication status	Published - 2009 May

Bibliographical note

Funding Information:
The research of the first author is supported by the grant KRF-2007-C00020. The research of the second author was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) KRF-2007-531-C00006. The research of third author is supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (Grant No. R01-2007-000-10527-0). The research of the fourth author is supported in part by the grant KOSEF-2007-8-1220. The fifth author was supported by a Korea University Grant.

Keywords

Hartree equation
Mass concentration
Mixed norm blow-up
Schrödinger equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1080/03605300902812426

Cite this

@article{c04b6c90af10403f9063a0ec960abf49,

title = "On mass concentration for the L2-critical nonlinear schrodinger equations",

abstract = "We consider the mass concentration phenomenon for the L2-critical nonlinear Schr{\"o}dinger equations. We show the mass concentration of blow-up solutions contained in LqtLrx space near the finite time. The new ingredient in this paper is a refinement of Strichartz's estimates with the mixed norm LqtLrx for 2",

keywords = "Hartree equation, Mass concentration, Mixed norm blow-up, Schr{\"o}dinger equation",

author = "M. Chae and S. Hong and J. Kim and S. Lee and Yang, {C. W.}",

note = "Funding Information: The research of the first author is supported by the grant KRF-2007-C00020. The research of the second author was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) KRF-2007-531-C00006. The research of third author is supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (Grant No. R01-2007-000-10527-0). The research of the fourth author is supported in part by the grant KOSEF-2007-8-1220. The fifth author was supported by a Korea University Grant.",

year = "2009",

month = may,

doi = "10.1080/03605300902812426",

language = "English",

volume = "34",

pages = "486--505",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "5",

}

TY - JOUR

T1 - On mass concentration for the L2-critical nonlinear schrodinger equations

AU - Chae, M.

AU - Hong, S.

AU - Kim, J.

AU - Lee, S.

AU - Yang, C. W.

N1 - Funding Information: The research of the first author is supported by the grant KRF-2007-C00020. The research of the second author was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) KRF-2007-531-C00006. The research of third author is supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (Grant No. R01-2007-000-10527-0). The research of the fourth author is supported in part by the grant KOSEF-2007-8-1220. The fifth author was supported by a Korea University Grant.

PY - 2009/5

Y1 - 2009/5

N2 - We consider the mass concentration phenomenon for the L2-critical nonlinear Schrödinger equations. We show the mass concentration of blow-up solutions contained in LqtLrx space near the finite time. The new ingredient in this paper is a refinement of Strichartz's estimates with the mixed norm LqtLrx for 2

AB - We consider the mass concentration phenomenon for the L2-critical nonlinear Schrödinger equations. We show the mass concentration of blow-up solutions contained in LqtLrx space near the finite time. The new ingredient in this paper is a refinement of Strichartz's estimates with the mixed norm LqtLrx for 2

KW - Hartree equation

KW - Mass concentration

KW - Mixed norm blow-up

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=68949205618&partnerID=8YFLogxK

U2 - 10.1080/03605300902812426

DO - 10.1080/03605300902812426

M3 - Article

AN - SCOPUS:68949205618

SN - 0360-5302

VL - 34

SP - 486

EP - 505

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 5

ER -