Unique Continuation Principles for the Benjamin-Ono Equation

Rafael José Iorio Jr.

Keywords: Benjamin-Ono | Unique continuation | Hilbert transform

Let $\sigma $ denote the Hilbert transform and $\mu \geq 0$. We prove that if $u\in C\left( \left[ 0,T\right] ,H^{2}\left( \QTR{Bbb}{R}\right) \cap L_{2}^{2}\left( \QTR{Bbb}{R}\right) \right) $ is a solution of \EQN{6}{1}{}{0}{\RD{\CELL{\partial _{t}u+2\sigma \partial _{x}^{2}u+u\partial _{x}u=\mu \partial _{x}^{2}u}}{1}{}{}{}}such that there are $t_{1}

Anexos:

• A_77.ps