Dynamics for the focusing, energy-critical nonlinear Hartree equation
نویسندگان
چکیده
منابع مشابه
The Focusing Energy–critical Wave Equation
We survey recent results related to soliton resolution.
متن کاملGlobal well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case
We establish global existence, scattering for radial solutions to the energy-critical focusing Hartree equation with energy and Ḣ norm less than those of the ground state in R× R, d ≥ 5.
متن کاملOn the blow up phenomenon for the L-critical focusing Hartree equation in R
For the defocusing with 2 < γ < min(4, d), J. Ginibre and G. Velo [6] proved the global well-posedness and scattering results in the energy space. Later, K. Nakanishi [26] made use of a new Morawetz estimate to obtain the similar results for the more general functions V (x). Recently, the authors proved the global wellposedness and scattering for the defocusing, energy critical Hartree equation...
متن کاملOn the blow up phenomenon for the mass critical focusing Hartree equation in R
Here f(u) = λ ( V ∗|u|2 ) u, V (x) = |x|−γ , 0 < γ < d, and ∗ denotes the convolution in Rd. If λ > 0, we call the equation (1.1) defocusing; if λ < 0, we call it focusing. This equation describes the mean-field limit of many-body quantum systems; see, e.g., [6], [7] and [36]. An essential feature of Hartree equation is that the convolution kernel V (x) still retains the fine structure of micro...
متن کاملThe Cauchy problem for the L-critical focusing Hartree equation in three dimensions
For the defocusing, energy subcritical case, J. Ginibre and G. Velo [8] proved the global well-posedness and scattering results in the energy space. Later, K. Nakanishi [25] made use of a new Morawetz estimate to obtain the similar results for the more general functions V (x). Recently, the authors proved the global wellposedness and scattering for the defocusing, energy critical Hartree equati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2015
ISSN: 0933-7741,1435-5337
DOI: 10.1515/forum-2011-0087