Global Existence of Solutions for the Cauahy Problem of the Kawahara Equation with $L^2$ Initial Data     Kawahara equation  Cauchy problem  global solution       font style='font-size:12px;'> 2007/12/11

In this paper we study solvability of the Cauchy problem of the Kawahara equation $\partial_tu+au\partial_xu+\beta\partial^3_xu+\gamma\partial^5_xu =0$ with $L^2$ initial data. By working on the Bourg...

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Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices     Kawahara equation    Cauchy problem    global solution    almost conservation law       font style='font-size:12px;'> 2007/12/11

We first prove that the Cauchy problem of the Kawahara equation, $\partial_tu+u\partial_xu+\beta\partial_x^3u+\gamma\partial_x^5u=0,$ is locally solvable if the initial data belong to $H^{r}(\bf{R})...

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