Development of singularities for the compressible Euler equations with external force in several dimensions

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dc.creatorRozanova, Olga
dc.date2004-11-30
dc.date2004-12-01
dc.date.accessioned2026-07-07T09:42:16Z
dc.date.available2026-07-07T09:42:16Z
dc.descriptionWe consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0411652
dc.identifierhttp://arxiv.org/abs/math/0411652
dc.identifierJournal of Mathematical Sciences, Vol. 143, No. 4, 2007
dc.identifierdoi:10.1007/s10958-007-0214-2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162122
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35L65;35L60;35L67
dc.titleDevelopment of singularities for the compressible Euler equations with external force in several dimensions
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