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Well-posedness and persistence properties for the Novikov equation. (English) Zbl 1215.37051

The authors prove that the Cauchy problem for the Novikov equation

t u- t x 2 u+4u 2 x u=3u x u x 2 u+u 2 x 3 u,u(0)=u 0 ,

is locally well-posed in the Besov spaces B 2,r 3/2 and in the Sobolev spaces H s with s>3/2. Some persistence properties for the strong solution of the above problem are also established.

MSC:
37L05General theory, nonlinear semigroups, evolution equations
35Q53KdV-like (Korteweg-de Vries) equations
26A12Rate of growth of functions of one real variable, orders of infinity, slowly varying functions
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