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

Author(s): Feride Tiglay
Journal: Trans. Amer. Math. Soc. 360 (2008), 1861-1877.
MSC (2000): Primary 35Q53, 35Q05, 35A10, 37K65
Posted: November 19, 2007
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Abstract: We prove that the periodic initial value problem for a modified Euler-Poisson equation is well-posed for initial data in $ H^{s}(\mathbb{T}^{m})$ when $ s>m/2+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 $ \mathrm{Diff} \ltimes C^{\infty}(\mathbb{T})$ as a Hamiltonian equation, we concentrate on one space dimension ($ m=1$) and show that the equation is bihamiltonian.

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Additional Information:

Feride Tiglay
Affiliation: Department of Mathematics, University of New Orleans, Lake Front, New Orleans, Louisiana 70148

DOI: 10.1090/S0002-9947-07-04248-1
PII: S 0002-9947(07)04248-1
Received by editor(s): October 15, 2004
Received by editor(s) in revised form: June 9, 2005 and October 13, 2005
Posted: November 19, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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