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Global well-posedness for KdV in Sobolev spaces of negative index. (English) Zbl 0967.35119
Summary: The initial value problem for the Korteweg-de Vries equation on the line $$\partial_t u+\partial^3_x u+\textstyle{{1\over 2}} \partial_x(u^2)= 0,\quad x\in\bbfR,$$ $$u(0)= \phi$$ is shown to be globally well-posed for rough data $\phi$. In particular, we show global well-posedness for initial data in $H^s(\bbfR)$ for $-3/10< s$.

35Q53KdV-like (Korteweg-de Vries) equations
35A05General existence and uniqueness theorems (PDE) (MSC2000)
42B35Function spaces arising in harmonic analysis
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
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