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A one-dimensional inviscid and compressible fluid in a harmonic potential well
EPFL, Lausanne.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2007 (English)In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 99, no 2, p. 161-183Article in journal (Refereed) Published
Abstract [en]

A Hamiltonian model is analyzed for a one-dimensional inviscid compressible fluid. The space-time evolution of the fluid is governed by the following system of the Hamilton-Jacobi and the continuity equations: S-t + 1/2(S-x(2) + omega(2)chi(2)) =0, S(x, 0) = S-0(x); rho(t) + (rho S-x)(x) =0, rho(x, 0) =rho(0)(x).Here S and rho designate the velocity potencial and the mass density, respectively. Unless S-0 is convex, shocks form and the velocity S (x) becomes discontinuous in {0 < omega t < pi/2}. It is demonstrated that there nevertheless exists a unique viscosity-measure solution (S,rho) when S-0 is globally Lipschitz continuous and locally semi-concave while rho(0) is a finite Borel measure. The structure of the velocity and the density is exhibited. For initial data correlated in a certain sense, a class of classical solutions (S,rho) is given. Negative time is also considered, and illustrating examples are given.

Place, publisher, year, edition, pages
2007. Vol. 99, no 2, p. 161-183
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-10892DOI: 10.1007/s10440-007-9161-7ISI: 000250403800002Scopus ID: 2-s2.0-35548982191Local ID: 9c51f860-6b47-11dc-9e58-000ea68e967bOAI: oai:DiVA.org:ltu-10892DiVA, id: diva2:983840
Note
Validerad; 2007; 20070925 (strom)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Strömberg, Thomas

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