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            <title xml:lang="en">KORTEWEG-DE VRIES AND BENJAMIN-ONO EQUATIONS ON ZHIDKOV SPACES</title>
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              <p>Motivated by the study of the Cauchy problem with bore-like initial data, we show the "well-posedness" for Korteweg-de Vries and Benjamin-Ono equations with initial data in Zhidkov spaces X s , with respectively s &gt; 1 and s &gt; 5/4. Here, "well-posedness" includes local (global in some cases) existence, uniqueness under a supplementary assumption, and continuity with respect to the initial data.</p>
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