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Solutions to the Korteweg-de Vries equation with irregular initial profile. (English) Zbl 0606.35079

The initial value problem for the Korteweg-de Vries equation is proved to possess unique regular solutions u(x,t), \(t>0\), for irregular initial data \(u(x,0)=v\) such that \(\int^{\infty}_{-\infty}(1+| x|^ N)d| v| (x)<\infty\). Here v is a measure defined on the Borel sets of R. The main point of the proof is the existence proof of solutions of the corresponding Marchenko equation.
Reviewer: E.Malec

MSC:

35R05 PDEs with low regular coefficients and/or low regular data
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
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References:

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