A Sharp Bilinear Estimate for the Bourgain-type Space with Application to the Benjamin Equation
نویسندگان
چکیده
This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/illposedness of the Cauchy problem for the Benjamin equation.
منابع مشابه
Bilinear Space-time Estimates for Linearised Kp-type Equations on the Three-dimensional Torus with Applications
A bilinear estimate in terms of Bourgain spaces associated with a linearised Kadomtsev-Petviashvili-type equation on the three-dimensional torus is shown. As a consequence, time localized linear and bilinear space time estimates for this equation are obtained. Applications to the local and global well-posedness of dispersion generalised KP-II equations are discussed. Especially it is proved tha...
متن کاملOn the low regularity of the fifth order Kadomtsev-Petviashvili I equation
We consider the fifth order Kadomtsev-Petviashvili I (KP-I) equation as ∂tu + α∂ 3 xu + ∂ 5 xu + ∂ −1 x ∂ 2 yu + uux = 0, while α ∈ R. We introduce an interpolated energy space Es to consider the well-posedeness of the initial value problem (IVP) of the fifth order KP-I equation. We obtain the local well-posedness of IVP of the fifth order KP-I equation in Es for 0 < s ≤ 1. To obtain the local ...
متن کاملGlobal solutions for the Dirac-Klein-Gordon system in two space dimensions
The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L Schrödinger data and wave data in H 1 2 ×H − 1 2 . In the case of smooth data there exists a global smooth (classical) solution. The proof uses function spaces of Bourgain type based on Besov spaces – previously applied by Colliander, Kenig and Staffilani for generalized Benjamin-...
متن کاملLow regularity solutions of two fifth-order KdV type equations
The Kawahara and modified Kawahara equations are fifth-order KdV type equations and have been derived to model many physical phenomena such as gravitycapillary waves and magneto-sound propagation in plasmas. This paper establishes the local well-posedness of the initial-value problem for Kawahara equation in H(R) with s > − 4 and the local well-posedness for the modified Kawahara equation in H(...
متن کاملSolitons And Periodic Solutions To The Generalized Zakharov-Kuznetsov Benjamin-Bona-Mahoney Equation
This paper studies the generalized version of theZakharov-Kuznetsov Benjamin-Bona-Mahoney equation. The functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. There are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. The results of this pape...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009