论文标题
BESOV空间中的分数Camassa-Holm方程的Cauchy问题
The Cauchy problem for fractional Camassa-Holm equation in Besov space
论文作者
论文摘要
在本文中，我们考虑了对非局限性和非线性弹性培养基中小而纤维的单向波的传播的分数camassa-holm方程。首先，我们在besov space中建立本地供应良好的度，$ b^{s_0} _ {2,1} $，$ s_0 =2ν-\ frac 1 2 $ for $ν> \ frac 3 2 $和$ s_0 = \ frac 5 2 $ for $ 1 <νν才能\ teq \ leq \ freac 3 2 $。然后，使用给定的分析初始数据，我们在两个变量中建立了解决方案的分析性，在空间和本地及时地建立了解决方案。
In this paper, we consider the fractional Camassa-Holm equation modelling the propagation of small-but-finite amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. First, we establish the local well-posedness in Besov space $B^{s_0}_{2,1}$ with $s_0=2ν-\frac 1 2$ for $ν>\frac 3 2 $ and $s_0=\frac 5 2$ for $1<ν\leq \frac 3 2 $. Then, with a given analytic initial data, we establish the analyticity of the solutions in both variables, globally in space and locally in time.
