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

Gang Wu, and Jia Yuan. "Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces." Applicationes Mathematicae 34.3 (2007): 253-267. <http://eudml.org/doc/279663>.

@article{GangWu2007,
abstract = {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.},
author = {Gang Wu, Jia Yuan},
journal = {Applicationes Mathematicae},
keywords = {the generalized Camassa--Holm equation; Cauchy problem; local well-posedness; Besov spaces; Littlewood–Paley theory},
language = {eng},
number = {3},
pages = {253-267},
title = {Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces},
url = {http://eudml.org/doc/279663},
volume = {34},
year = {2007},
}

TY - JOUR
AU - Gang Wu
AU - Jia Yuan
TI - Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces
JO - Applicationes Mathematicae
PY - 2007
VL - 34
IS - 3
SP - 253
EP - 267
AB - 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.
LA - eng
KW - the generalized Camassa--Holm equation; Cauchy problem; local well-posedness; Besov spaces; Littlewood–Paley theory
UR - http://eudml.org/doc/279663
ER -