The Cauchy problem and integrability of a modified Euler-Poisson equation

2005/01/18 by Feride Tığlay, Feride Tiglay, Tiglay, Feride
Mathematics · Physics and Astronomy · #35A10 #35Q05 #35Q53 #37K65 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #math.AP #msc:35A10 #msc:35Q05 #msc:35Q53 #msc:37K65

paper · pdf · doi:10.48550/arxiv.math/0501279

submitted

openalex publication_date 2005/01/18 · arxiv created 2006/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the periodic initial value problem for a modified Euler-Poisson equation is well-posed for initial data in H^s (T^m) when s>m/2+2 and we improve the Sobolev index to s>3/2 for m=1. We also study the analytic regularity of this problem and prove a Cauchy-Kowalevski type theorem. After presenting a formal derivation of the equation on the semidirect product space Diff \ltimes C^∞(\tor) as a Hamiltonian equation, we concentrate to one space dimension (m=1) and show that the equation is bihamiltonian.

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