带立方非线性修正 Camassa-Holm 方程的初值问题

Abstract

Abstract:

In this paper, by Kato's theory of semigroup and the definition of the dissipative operator, we study the initial value problem of a modified Camassa-Holm equation with cubic nonlinearity, and establish the existence and uniqueness of its solutions in Sobolev space $ H^{s,p}(\mathbb{R}) $, $ s\ge 1 $, $ p\in (1,\infty ) $, which extend the well-posedness of its solutions in Besov space $ B_{p,r}^{s}(\mathbb{R}) $ $ (p,\ r\ge 1,\ s> \max \{2+\frac{1}{p},\frac{5}{2}\}) $ obtained by Fu et al. (J Differ Equations, 2013, 255: 1905-1938).

Key words: The modified Camassa-Holm equation, Well-posedness, Dissipative operator, Kato's theory of semigroup

CLC Number:

O175.2

Zhang Xin, Wu Xinglong. The Initial Value Problem for a Modified Camassa-Holm Equation with Cubic Nonlinearity[J].Acta mathematica scientia,Series A, 2024, 44(2): 376-383.

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References

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The Initial Value Problem for a Modified Camassa-Holm Equation with Cubic Nonlinearity

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