Abstract
In this paper, we are concerned with the Cauchy problem for the modified Novikov equation. By using the transport equation theory and Littlewood-Paley decomposition as well as nonhomogeneous Besov spaces, we prove that the Cauchy problem for the modified Novikov equation is locally well posed in the Besov space with and and show that the Cauchy problem for the modified Novikov equation is locally well posed in the Besov space with the aid of Osgood lemma. MSC: 35G25, 35L05, 35R25.
Highlights
Zhao and Zhou [ ] considered the exact traveling wave solution to the following modified Novikov equation: ut – utxx + u ux = uuxuxx + u uxxx. ( . )We recall that the Novikov equation ut – utxx = u uxxx + uuxuxx – u ux was discovered by Vladimir Novikov [ ] and it possesses the bi-Hamiltonian structure, infinite conservation laws
The well-posedness and blow-up of the Cauchy problem for the Novikov equation in Sobolev spaces and Besov spaces have been investigated by some authors [ – ]
The weak solution of the Cauchy problem for the Novikov equation has been investigated by some authors [, ]
Summary
Zhao and Zhou [ ] considered the exact traveling wave solution to the following modified Novikov equation: ut – utxx + u ux = uuxuxx + u uxxx. We recall that the Novikov equation ut – utxx = u uxxx + uuxuxx – u ux was discovered by Vladimir Novikov [ ] and it possesses the bi-Hamiltonian structure, infinite conservation laws. The well-posedness and blow-up of the Cauchy problem for the Novikov equation in Sobolev spaces and Besov spaces have been investigated by some authors [ – ]. The weak solution of the Cauchy problem for the Novikov equation has been investigated by some authors [ , , ]. Li and Yan [ ] considered the Cauchy problem for the KdV equation with higher dispersion
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