Wyniki wyszukiwania

1

Global well-posedness and blow up for the nonlinear fractional beam equations

100%

Ma S., Xu G.

Applicationes Mathematicae

|

2010

|

tom 37

|

nr 3

353-373

EN

We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.

2

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

81%

Miao C., Xu G., Zhao L.

Colloquium Mathematicum

|

2009

|

tom 114

|

nr 2

213-236

EN

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.

3

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

81%

Miao C., Xu G., Zhao L.

Colloquium Mathematicum

|

2010

|

tom 119

|

nr 1

23-50

EN

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

1 Applicationes Mathematicae

3 Xu G.

2 Miao C.

2 Zhao L.

1 Ma S.

2 2010

1 2009

Global well-posedness and blow up for the nonlinear fractional beam equations

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