Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces

• Autorzy: Gang Wu , Jia Yuan
• Języki publikacji: EN

Abstrakty

EN

We study local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation $∂_{t}u - ∂³_{txx}u + 2κ∂_{x}u + ∂_{x}[g(u)/2] = γ(2∂_{x}u∂²_{xx}u + u∂³_{xxx}u)$ for the initial data u₀(x) in the Besov space $B^{s}_{p,r}(ℝ)$ with max(3/2,1 + 1/p) < s ≤ m and (p,r) ∈ [1,∞]², where g:ℝ → ℝ is a given $C^{m}$-function (m ≥ 4) with g(0)=g'(0)=0, and κ ≥ 0 and γ ∈ ℝ are fixed constants. Using estimates for the transport equation in the framework of Besov spaces, compactness arguments and Littlewood-Paley theory, we get a local well-posedness result.

Kategorie tematyczne

• 35G25: Initial value problems for nonlinear higher-order equations
• 35Q35: PDEs in connection with fluid mechanics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2007
• Tom: 34
• Numer: 3
• Strony: 253-267

Daty

wydano

2007

Twórcy

autor

Gang Wu

• The Graduate School of China Academy of Engineering Physics, P.O. Box 2101, Beijing 100088, China

autor

Jia Yuan

• The Graduate School of China Academy of Engineering Physics, P.O. Box 2101, Beijing 100088, China

Identyfikatory

DOI

10.4064/am34-3-1