THE CAUCHY PROBLEM FOR THE CAMASSA-HOLM-NOVIKOV EQUATION*

doi:10.1007/s10473-023-0220-6

Abstract

Abstract: In this paper, we consider the Cauchy problem for the Camassa-Holm-Novikov equation. First, we establish the local well-posedness and the blow-up scenario. Second, infinite propagation speed is obtained as the nontrivial solution $u(x,t)$ does not have compact $x$-support for any $t>0$ in its lifespan, although the corresponding $u_0(x)$ is compactly supported. Then, the global existence and large time behavior for the support of the momentum density are considered. Finally, we study the persistence property of the solution in weighted Sobolev spaces.

Key words: Camassa-Holm-Novikov equation, local well-posedness, blow-up scenario, infinite propagation speed, global existence, large time behavior, persistence property

Mingxuan Zhu, Zaihong Jiang. THE CAUCHY PROBLEM FOR THE CAMASSA-HOLM-NOVIKOV EQUATION^*[J].Acta mathematica scientia,Series B, 2023, 43(2): 736-750.

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THE CAUCHY PROBLEM FOR THE CAMASSA-HOLM-NOVIKOV EQUATION^*

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