Well-posedness for the fifth order KdV equation

Details Well-posedness for the fifth order KdV equation Well-posedness for the fifth order KdV equation

2010-11-17

arxiv.org/abs/1011.3956v2

Mathematics

Analysis of PDEs

Scientific paper

In this paper, we establish the well-posedness for the Cauchy problem of the fifth order KdV equation with low regularity data. The nonlinear term has more derivatives than can be recovered by the smoothing effect, which implies that the iteration argument is not available when initial data is given in $H^s$ for any $s \in \mathbb{R}$. So we give initial data in $H^{s,a}=H^s \cap \dot{H}^a$ when $a \leq s$ and $a \leq 0$. Then we can use the Fourier restriction norm method to obtain the local well-posedness in $H^{s,a}$ when $s \geq \max\{-1/4, -2a-2 \}$, $-3/2

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