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November/December 2019 On the Cauchy problem for the periodic fifth-order KP-I equation
Tristan Robert
Differential Integral Equations 32(11/12): 679-704 (November/December 2019).

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.

Citation

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Tristan Robert. "On the Cauchy problem for the periodic fifth-order KP-I equation." Differential Integral Equations 32 (11/12) 679 - 704, November/December 2019.

Information

Published: November/December 2019
First available in Project Euclid: 22 October 2019

zbMATH: 07144909
MathSciNet: MR4021259

Subjects:
Primary: 35Q35, 35Q53

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 11/12 • November/December 2019
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