On the blow-up phenomenon for the mass-critical focusing Hartree equation in ℝ⁴
Changxing Miao ; Guixiang Xu ; Lifeng Zhao
Colloquium Mathematicae, Tome 120 (2010), p. 23-50 / Harvested from The Polish Digital Mathematics Library
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We characterize the dynamics of the finite time blow-up solutions with minimal mass for the focusing mass-critical Hartree equation with H¹(ℝ⁴) data and L²(ℝ⁴) data, where we make use of the refined Gagliardo-Nirenberg inequality of convolution type and the profile decomposition. Moreover, we analyze the mass concentration phenomenon of such blow-up solutions.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:283550 
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     author = {Changxing Miao and Guixiang Xu and Lifeng Zhao},
     title = {On the blow-up phenomenon for the mass-critical focusing Hartree equation in R4},
     journal = {Colloquium Mathematicae},
     volume = {120},
     year = {2010},
     pages = {23-50},
     zbl = {1193.35211},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-2}
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Changxing Miao; Guixiang Xu; Lifeng Zhao. On the blow-up phenomenon for the mass-critical focusing Hartree equation in ℝ⁴. Colloquium Mathematicae, Tome 120 (2010) pp. 23-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-1-2/