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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

${\partial }_{t}u-{\partial }_{t}{\partial }_{x}^{2}u+4{u}^{2}{\partial }_{x}u=3u{\partial }_{x}u{\partial }_{x}^{2}u+{u}^{2}{\partial }_{x}^{3}u,\phantom{\rule{1.em}{0ex}}u\left(0\right)={u}_{0},$

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:
 37L05 General theory, nonlinear semigroups, evolution equations 35Q53 KdV-like (Korteweg-de Vries) equations 26A12 Rate of growth of functions of one real variable, orders of infinity, slowly varying functions
##### References:
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