论文标题
批评空间中广义camassa-holm方程的本地良好性的新结果
A new result for the local well-posedness of the generalized Camassa-Holm equations in critial Besov spaces $B^{\frac{1}{p}}_{p,1},1\leq p<+\infty$
论文作者
论文摘要
本文致力于研究批评性的camassa-holm方程的当地良好（存在，独特性和连续依赖性），批评性besov spaces $ b^{\ frac {\ frac {1} {p}}} {p}} _ {p，1} $ a {p，1} $，带有$ 1 \ leq p <+leq p <+\ f+\ f index $ \ max \ {\ frac {1} {2}，\ frac {1} {p} \} $或$ s = \ frac {1} {1} {p}，\ p \ in [1,2]，\ r = 1 $ in \ cite {linb，tu-yin4}。主要困难是证明需要使用Moser型不平等的唯一性。为了克服困难，我们使用拉格朗日坐标转换来获得独特性。
This paper is devoted to studying the local well-posedness (existence,uniqueness and continuous dependence) for the generalized Camassa-Holm equations in critial Besov spaces $B^{\frac{1}{p}}_{p,1}$ with $1\leq p<+\infty$, which improves the previous index $s> \max\{\frac{1}{2},\frac{1}{p}\}$ or $s=\frac{1}{p},\ p\in[1,2],\ r=1$ in \cite{linb,tu-yin4}. The main difficulty is to prove the uniqueness, which need to use the Moser-type inequality. To overcome the difficulty, we use the Lagrange coordinate transformation to obtain the uniqueness.
