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

• Autorzy: Changxing Miao , Guixiang Xu , Lifeng Zhao
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 47J35: Nonlinear evolution equations
• 35Q55: NLS-like equations (nonlinear Schr\"odinger)
• 35Q40: PDEs in connection with quantum mechanics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 119
• Numer: 1
• Strony: 23-50

Daty

wydano

2010

Twórcy

autor

Changxing Miao

• Institute of Applied Physics and, Computational Mathematics, P.O. Box 8009, Beijing, China, 100088

autor

Guixiang Xu

• Institute of Applied Physics and, Computational Mathematics, P.O. Box 8009, Beijing, China, 100088

autor

Lifeng Zhao

• Department of Mathematics, University of Science and Technology of China

Identyfikatory

DOI

10.4064/cm119-1-2