SeMA Journal

pp 1–26 | Cite as

Computer-assisted proofs in PDE: a survey

  • Javier Gómez-SerranoEmail author


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.


PDE Computer-assisted Singularity Incompressible 

Mathematics Subject Classification

Primary 65G30 Secondary 35Q35 35R35 



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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