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

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 $\mathbb{E} = \{u\in L^2,~\partial_x^2 u \in L^2,~\partial_x^{-1}\partial_y u \in L^2\}$ which is the natural energy space associated with this equation.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-01761459
Contributor : Tristan Robert <>
Submitted on : Monday, April 9, 2018 - 10:41:15 AM
Last modification on : Thursday, May 3, 2018 - 3:18:02 PM

### Identifiers

• HAL Id : hal-01761459, version 1
• ARXIV : 1712.01134

### Citation

Tristan Robert. On the Cauchy problem for the periodic fifth-order KP-I equation. 2018. ⟨hal-01761459⟩

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