dc.contributor.author
Buckmaster, T.
dc.contributor.author
Cao-Labora, G.
dc.contributor.author
Gómez-Serrano, J.
dc.date.accessioned
2025-06-16T09:39:55Z
dc.date.available
2025-06-16T09:39:55Z
dc.date.issued
2025-02-12
dc.identifier.uri
http://hdl.handle.net/2072/484446
dc.description.abstract
Building upon the pioneering work of Merle, Raphaël, Rodnianski and Szeftel [67, 68, 69], we construct exact, smooth self-similar imploding solutions to the 3D isentropic compressible Euler equations for ideal gases for all adiabatic exponents 1$ ]]>. For the particular case (corresponding to a diatomic gas - for example, oxygen, hydrogen, nitrogen), akin to the result [68], we show the existence of a sequence of smooth, self-similar imploding solutions. In addition, we provide simplified proofs of linear stability [67] and nonlinear stability [69], which allow us to construct asymptotically self-similar imploding solutions to the compressible Navier-Stokes equations with density independent viscosity for the case. Moreover, unlike [69], the solutions constructed have density bounded away from zero and converge to a constant at infinity, representing the first example of singularity formation in such a setting.
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dc.description.sponsorship
T.B. was supported by the NSF grant DMS-1900149, a Simons Foundation Mathematical and Physical Sciences CollaborativeGrant and a grant from the Institute forAdvanced Study. G.C.-L.was supported by a grant from the Centre de Formacio Interdisciplinaria Superior, a MOBINT-MIF grant from the Generalitat de Catalunya, a Praecis Presidential Fellowship from the Massachusetts Institute of Technology and NSF grants DMS-2052651 and DMS-1764403. G.C.-L. would also like to thank the Department of Mathematics at Princeton University for partially supporting him during his stay at Princeton and for their warm hospitality. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program through the grant agreement 852741 (G.C.-L. and J.G.-S.). G.C-L. and J.G.-S. have been partially supported by the MICINN (Spain) research grant number PID2021–125021NA–I00. J.G.-S. was partially supported by NSF through Grants DMS-1763356, DMS-2245017 and DMS-2247537. J.G.-S has been partially supported by the AGAUR project 2021-SGR-0087 (Catalunya). This material is based upon work supported by the National Science Foundation under Grant No. DMS-1929284 while J.G.-S. was in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the program ‘Hamiltonian Methods in Dispersive and Wave Evolution Equations’. This work is supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M).We thank Princeton University and the Institute for Advanced Study for computing facilities via the Princeton Research Computing resources and the School of Natural Sciences Computing resources, respectively. Part of this research was conducted using computational resources and services at the Center for Computation and Visualization, Brown University. The programs ran on the batch queue: for more specific details about the hardware please check https://docs.ccv.brown.edu/oscar/system-overview.
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dc.format.extent
139 p.
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dc.publisher
Cambridge University Press
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dc.relation.ispartof
Forum of Mathematics, Pi
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dc.rights
© The Author(s) 2025
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dc.rights
Attribution 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Smooth imploding solutions
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dc.subject.other
Compressible fluids
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dc.title
Smooth imploding solutions for 3D compressible fluids
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1017/fmp.2024.12
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
