He first studied at École Polytechnique, where he worked on his PhD thesis advised by Haïm Brezis.

[1][2] His results concern partial differential equations related to fluid dynamics, with emphasis on nonlinear phenomena, and part of them found applications to control channels.

He had previously worked in the field of non-linear functional analysis, where he also obtained significant results.

[3] He is now a Professor at the University Pierre et Marie Curie in Paris, and a Senior member of the Institut Universitaire de France.

[4] Jean-Michel Coron is the husband of Claire Voisin who was also plenary speaker at the 2010 International Congress of Mathematicians and who is the 2016 recipient of the Gold medal of the French National Centre for Scientific Research, the highest scientific research award in France.