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The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices. (English) Zbl 0787.35090
The paper considers the initial value problem for the Korteweg-de Vries equation $$u\sb t+(u\sp 2)\sb x+u\sb{xxx}=0,\ t,x \in \bbfR,\ u(x,0)=u\sb 0(x), \tag 1 $$ for data in classical Sobolev spaces of negative order, i.e. $u\sb 0 \in H\sp{-s}(\bbfR)$ with $s \ge 0$. The main result shows that the problem (1) is locally well posed for $s<5/8$.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35K30Higher order parabolic equations, initial value problems
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References:
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