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SeMA Journal

pp 1–26 | Cite as

Computer-assisted proofs in PDE: a survey

  • Javier Gómez-SerranoEmail author
Article
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Abstract

In this survey we present some recent results concerning computer-assisted proofs in partial differential equations, focusing in those coming from problems in incompressible fluids. Particular emphasis is put on the techniques, as opposed to the results themselves.

Keywords

PDE Computer-assisted Singularity Incompressible 

Mathematics Subject Classification

Primary 65G30 Secondary 35Q35 35R35 

Notes

Acknowledgements

J.G.-S. was partially supported by the Grant MTM2014-59488-P (Spain), by the ICMAT-Severo Ochoa Grant SEV-2015-0554, by the Simons Collaboration Grant 524109 and by the NSF-DMS 1763356 Grant. We would like to thank Diego Córdoba, Jordi-Lluís Figueras and Francisco Gancedo for helpful comments on previous versions of this manuscript. This paper was developed out of a talk given at the XVIII Spanish-French School Jacques-Louis Lions about Numerical Simulation in Physics and Engineering, where I was awarded the 2018 Antonio Valle Prize from the Sociedad Española de Matemática Aplicada (SeMA). I would like to thank the SeMA and the organizers of the conference for such a great opportunity.

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© Sociedad Española de Matemática Aplicada 2019

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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