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  Local well-posedness for membranes in the light cone gauge

Allen, P. T., Andersson, L., & Restuccia, A. (2011). Local well-posedness for membranes in the light cone gauge. Communications in Mathematical Physics, 301(2), 383-410. doi:10.1007/s00220-010-1141-5.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-6530-C Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-6533-6
Genre: Journal Article

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0910.1488 (Preprint), 355KB
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 Creators:
Allen, Paul T.1, Author
Andersson, Lars2, Author              
Restuccia, Alvaro1, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, escidoc:24012              
2Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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Free keywords: High Energy Physics - Theory, hep-th,Mathematics, Analysis of PDEs, math.AP
 Abstract: In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian reduction gives a system with one constraint, the area preserving constraint. The Hamiltonian evolution equations corresponding to this system, however, fail to be hyperbolic. Making use of the area preserving constraint, an equivalent system of evolution equations is found, which is hyperbolic and has a well-posed initial value problem. We are thus able to solve the initial value problem for the Hamiltonian evolution equations by means of this equivalent system. We furthermore obtain a blowup criterion for the membrane evolution equations, and show, making use of the constraint, that one may achieve improved regularity estimates.

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Language(s): eng - English
 Dates: 2009-10-082011
 Publication Status: Published in print
 Pages: 29 pages
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 0910.1488
URI: http://arxiv.org/abs/0910.1488
DOI: 10.1007/s00220-010-1141-5
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Title: Communications in Mathematical Physics
Source Genre: Journal
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Publ. Info: Heidelberg : Springer-Verlag Heidelberg
Pages: - Volume / Issue: 301 (2) Sequence Number: - Start / End Page: 383 - 410 Identifier: ISSN: 0010-3616
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/954925392313