Local Analyticity in the Time and Space Variables and the Smoothing Effect for the Fifth‐Order KdV‐Type Equation

Kyoko Tomoeda

Advances in Mathematical Physics, 2011, vol. 2011, issue 1

Abstract: We consider the initial value problem for the reduced fifth‐order KdV‐type equation: ∂tu-∂x5u-10100∂x(u3)+∂x(∂xu) 2=, t, x ∈ ℝ, u(0, x) = ϕ(x), x ∈ ℝ. This equation is obtained by removing the nonlinear term 10u∂x3u from the fifth‐order KdV equation. We show the existence of the local solution which is real analytic in both time and space variables if the initial data ϕ ∈ Hs(ℝ) (s > 1/8) satisfies the condition ∑k=0∞(A0k/k!)∥(x∂x) kϕ∥Hs

Date: 2011
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https://doi.org/10.1155/2011/238138

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2011:y:2011:i:1:n:238138

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