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Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case

100%

Miao C., Xu G., Zhao L.

Colloquium Mathematicum

2009

tom 114

nr 2

213-236

We establish global existence and scattering for radial solutions to the energy-critical focusing Hartree equation with energy and Ḣ¹ norm less than those of the ground state in $ℝ × ℝ^{d}$, d ≥ 5.

On the blow-up phenomenon for the mass-critical focusing Hartree equation in ℝ⁴

100%

Miao C., Xu G., Zhao L.

Colloquium Mathematicum

2010

tom 119

nr 1

23-50

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.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Miao C.

2 Xu G.

2 Zhao L.

1 2010

1 2009

Wyniki wyszukiwania

Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case

On the blow-up phenomenon for the mass-critical focusing Hartree equation in ℝ⁴