Journal article
ON THE ISENTROPIC COMPRESSIBLE EULER EQUATION WITH ADIABATIC INDEX gamma=1
Pacific journal of mathematics, Vol.262(1), pp.109-128
03/01/2013
DOI: 10.2140/pjm.2013.262.109
Abstract
We consider the isentropic compressible Euler equations with polytropic gamma law P(rho) = rho(gamma) in dimensions d <= 3. We address the borderline case when adiabatic index gamma = 1 and establish local theory in the Sobolev space (CtLxp)-L-0 boolean AND C-t(0)(H) over dot(x)(k) for d < p <= 4. This covers a class of physical solutions which can decay to vacuum at spatial infinity and are not compact perturbations of steady states. We construct a blowup scenario where initially the fluid is quiet in a neighborhood of the origin but is supersonic near the spatial infinity. For this special class of noncompact initial data, we prove the formation of singularities in finite time.
Details
- Title: Subtitle
- ON THE ISENTROPIC COMPRESSIBLE EULER EQUATION WITH ADIABATIC INDEX gamma=1
- Creators
- Dong Li - Inst Adv Study, Princeton, NJ 08540 USAChangxing Miao - Inst Appl Phys & Computat Math, Beijing 100088, Peoples R ChinaXiaoyi Zhang - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Pacific journal of mathematics, Vol.262(1), pp.109-128
- Publisher
- PACIFIC JOURNAL MATHEMATICS
- DOI
- 10.2140/pjm.2013.262.109
- ISSN
- 0030-8730
- eISSN
- 1945-5844
- Number of pages
- 20
- Grant note
- NSERC; Natural Sciences and Engineering Research Council of Canada (NSERC) DMS-1128155 / NSF; National Science Foundation (NSF) 11171033; 11231006 / NSF of China; National Natural Science Foundation of China (NSFC) Alfred P. Sloan fellowship; Alfred P. Sloan Foundation
- Language
- English
- Date published
- 03/01/2013
- Academic Unit
- Mathematics
- Record Identifier
- 9984241155202771
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