## Differential and Integral Equations

### On the Cauchy problem for the periodic fifth-order KP-I equation

Tristan Robert

#### Abstract

The aim of this paper is to investigate the Cauchy problem for the periodic fifth order KP-I equation $${ \partial_t} u - { \partial_x}^5 u -{ \partial_x}^{-1} { \partial_y}^2u + u{ \partial_x} u = 0, ~(t,x,y)\in\mathbb R\times\mathbb T^2 .$$ We prove global well-posedness for constant $x$ mean value initial data in the space $\mathbf E = \{u\in L^2,~{ \partial_x}^2 u \in L^2, ~{ \partial_x}^{-1} { \partial_y} u \in L^2\}$ which is the natural energy space associated with this equation.

#### Article information

Source
Differential Integral Equations, Volume 32, Number 11/12 (2019), 679-704.

Dates
First available in Project Euclid: 22 October 2019