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On the Cauchy problem for the periodic fifth-order KP-I equation (1712.01134v1)
Published 4 Dec 2017 in math.AP
Abstract: The aim of this paper is to investigate the Cauchy problem for the periodic fifth order KP-I equation [\partial_t u - \partial_x5 u -\partial_x{-1}\partial_y2u + u\partial_x u = 0,~(t,x,y)\in\mathbb{R}\times\mathbb{T}2] We prove global well-posedness for constant $x$ mean value initial data in the space $\mathbb{E} = {u\in L2,~\partial_x2 u \in L2,~\partial_x{-1}\partial_y u \in L2}$ which is the natural energy space associated with this equation.