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 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<q≤r.
Original language | English |
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Pages (from-to) | 486-505 |
Number of pages | 20 |
Journal | Communications in Partial Differential Equations |
Volume | 34 |
Issue number | 5 |
DOIs | |
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