Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces
Gang Wu ; Jia Yuan
Applicationes Mathematicae, Tome 34 (2007), p. 253-267 / Harvested from The Polish Digital Mathematics Library
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We study local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation ∂tu-∂³txxu+2κ∂xu+∂x[g(u)/2]=γ(2∂xu∂²xxu+u∂³xxxu) for the initial data u₀(x) in the Besov space Bp,rs(ℝ) with max(3/2,1 + 1/p) < s ≤ m and (p,r) ∈ [1,∞]², where g:ℝ → ℝ is a given Cm-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.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:279663 
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Gang Wu; Jia Yuan. Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces. Applicationes Mathematicae, Tome 34 (2007) pp. 253-267. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-1/