Well-posedness for the fifth-order KdV equation in the energy space

2012/05/01 by Kenig, Carlos E., Pilod, Didier
#35A01 #35Q35 #35Q53 #37K05 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1205.0169

Abstract

We prove that the initial value problem (IVP) associated to the fifth order KdV equation equation ∂_tu-α∂⁵_x u=c₁∂_xu∂_x²u+c₂∂_x(u∂_x²u)+c₃∂_x(u³), equation where x ∈ \mathbb R, t ∈ \mathbb R, u=u(x,t) is a real-valued function and α, c₁, c₂, c₃ are real constants with α≠ 0, is locally well-posed in H^s(\mathbb R) for s ≥ 2. In the Hamiltonian case (\textit i.e. when c₁=c₂), the IVP associated to \eqref05KdV is then globally well-posed in the energy space H²(\mathbb R).

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