Benjamin-Ono方程的初值问题与线性化问题的准确解

The Initial Value Problem for Benjamin-Ono Equation and the Exact Solution to the Linearized Problem

本文证明了 Benjamin—Ono 方程初值问题解的唯一性与稳定性;借助 Fourier 变换求出了线性化的 B—O 方程初值问题的准确解,即积分表达式,当初值函数充分光滑且在无穷远处趋于零时,问题的古典解存在.

In the present paper,the uniqueness and stability of the solution ofinitial value problem for the Benjamin-Ono equation is proved.The exactsolution,i.e.,the integral representation of the solution of initial valueproblem for linearized B-O equation is given by means of Fourier transform.If the initial value function and its derivatives approach to zero rapidlyas |x|→∞,there exists classical solution to the problem.