Scattering for defocusing generalized Benjamin-Ono equation in the energy space $H^{\frac {1}{2}}(\mathbb {R})$
نویسندگان
چکیده
منابع مشابه
Singularity Formation in the Generalized Benjamin-ono Equation
A Fourier-collocation scheme is used to approximate solutions to the generalized Benjamin-Ono equation ut +uux −Huxx = 0. The numerical simulation suggests that the equation features smooth solutions that become unbounded in finite time.
متن کاملGlobal well-posedness in the Energy space for the Benjamin-Ono equation on the circle
We prove that the Benjamin-Ono equation is well-posed in H(T). This leads to a global well-posedeness result in H(T) thanks to the energy conservation. Résumé. Nous montrons que l’équation de Benjamin-Ono est bien posée dans H(T). Il découle alors de la conservation de l’énergie que la solution existe pour tout temps dans cette espace.
متن کاملSolitary waves of the rotation-generalized Benjamin-Ono equation
This work studies the rotation-generalized Benjamin-Ono equation which is derived from the theory of weakly nonlinear long surface and internal waves in deep water under the presence of rotation. It is shown that the solitary-wave solutions are orbitally stable for certain wave speeds.
متن کاملPerturbation theory for the Benjamin–Ono equation
We develop a perturbation theory for the Benjamin–Ono (BO) equation. This perturbation theory is based on the inverse scattering transform for the BO equation, which was originally developed by Fokas and Ablowitz and recently refined by Kaup and Matsuno. We find the expressions for the variations of the scattering data with respect to the potential, as well as the dual expression for the variat...
متن کاملGlobal well-posedness and scattering for the energy-critical, defocusing Hartree equation in R
We obtain global well-posedness, scattering, uniform regularity, and global L t L 6n 3n−8 x spacetime bounds for energy-space solutions to the defocusing energycritical nonlinear Hartree equation in R× R, n ≥ 5.
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: Transactions of the American Mathematical Society
سال: 2019
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7831