Mathematics – Analysis of PDEs
Scientific paper
2009-10-30
Mathematics
Analysis of PDEs
33 pages
Scientific paper
We prove that the Kawahara equation is locally well-posed in $H^{-7/4}$ by using the ideas of $\bar{F}^s$-type space \cite{GuoKdV}. Next we show it is globally well-posed in $H^s$ for $s\geq -7/4$ by using the ideas of "I-method" \cite{I-method}. Compared to the KdV equation, Kawahara equation has less symmetries, such as no invariant scaling transform and not completely integrable. The new ingredient is that we need to deal with some new difficulties that are caused by the lack symmetries of this equation.
Chen Wengu
Guo Zihua
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